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Case Study Questions Class 7 Maths Integers

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CBSE Important Questions Class 7 Maths Chapter 1

Home » CBSE » CBSE Important Questions Class 7 Maths Chapter 1

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Important Questions Class 7 Mathematics Chapter 1 – Integers

Mathematics is an important subject that we need in our daily life too. Students must solve questions to clear their concepts and boost their confidence. The first chapter of Class 7 Mathematics under CBSE curriculum is integers.

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Students have learned integers in their previous class. In this chapter, they will learn how to put the integers on the number line, their properties, and the addition and multiplication of integers. It is a very important chapter. Students must practice the textbook exercise and questions from other sources to build their concepts.

Extramarks is a leading company that provides a wide range of study materials related to CBSE and NCERT. Our experts have made the Important Questions Class 7 Mathematics Chapter 1 to help students in regular practice. They collected the questions from different sources such as the textbook exercises, CBSE sample papers, CBSE past years’ question papers and important reference books. They have solved the questions too. Hence, the question series will help students increase their exam marks.

Extramarks is a leading company that helps students by providing all the important study materials related to CBSE and NCERT. You may register on our official website and download these study materials. You will find the CBSE syllabus, NCERT textbooks, CBSE past years’ question papers, CBSE sample papers, CBSE revision notes, CBSE extra questions, NCERT solutions, NCERT important questions, vital formulas and many more.

Important Questions Class 7 Mathematics Chapter 1 – With Solutions

The experts of Extramarks have made this question series so that students can solve the questions daily. They collected the questions from the textbook exercises, CBSE sample papers and important reference books. They have included a few questions from the past years’ question papers so that students may have an idea regarding questions in exams. Experienced professionals have further checked the answers to ensure the best quality of the content. Thus, the Important Questions Class 7 Mathematics Chapter 1 will help students to score better in exams. The questions are-

Question 1. Following number line given below shows the temperature present in degree celsius at different places on a particular day.

Image Source: Internet / NCERT Textbook

(i) Observe the number line and write down the temperature of the places marked on it.

By observing the above number line, we can find out the temperature of the cities as follows,

The temperature in the city of Lahulspiti is -8°C.

The temperature in the city of Srinagar is -2°C

The temperature in the city of Shimla is 5°C.

The temperature in the city of Ooty is 14°C.

The temperature in the city of Bengaluru is 22°C.

(ii) What is the temperature difference between the hottest and the coldest places among the cities stated above?

From the above number line, we can observe that,

The temperature at the given hottest place, that is, Bengaluru, is 22°C.

The temperature at the given coldest place, that is, Lahulspiti, is -8°C

The temperature difference between the hottest and the coldest place is given as = 22°C – (-8°C)

= 22°C + 8°C

= 30° Celsius

Hence, the total temperature difference between the hottest and the coldest place is 30oC.

(iii) What is the temperature difference between the cities of Lahulspiti and Srinagar?

From the above-given number line,

∴The temperature difference between the cities Lahulspiti and Srinagar is = -2oC – (8oC)

= – 2°C + 8°C

(iv) Can we say that the temperature of Srinagar and Shimla taken together is less than the temperature present at Shimla? Is it also less than the temperature present at Srinagar?

The temperature in the city of Srinagar =-2°C

The temperature in the city of Shimla = 5°C

The temperature of the cities Srinagar and Shimla taken together becomes = – 2°C + 5°C

= 3° degree C

 5°C > 3°C

Hence, the temperature of the cities Srinagar and Shimla taken together is indeed less than the temperature present at Shimla.

3° > -2°

And No, the temperature of the cities Srinagar and Shimla taken together is not less than the temperature of the city Srinagar.

Question 2. Mohan deposits ₹ 2,000 in his bank account and then withdraws ₹ 1,642 from it the following day. Now, if the withdrawal of the amount from the account is represented by a negative integer, then how will you represent the total amount deposited? Also, Find the balance in Mohan’s account after the withdrawal.

Withdrawal of these amounts from the account is represented by a negative integer.

Then, the deposit of the amount to the account is represented by a positive integer.

From the above question,

The total amount that is deposited in the bank account by the Mohan = ₹ 2000

The total amount that is withdrawn from the bank account by the Mohan is = – ₹ 1642

Final Balance in Mohan’s account after the withdrawal = amount deposited + amount is withdrawn

= ₹ 2000 + (-₹ 1642)

= ₹ 2000 – ₹ 1642

Hence, the total balance in Mohan’s account after the withdrawal is ₹ 358

Question 3. In the following quiz, positive marks are given for every correct answer and negative marks are given for each incorrect answer. If Jack’s scores in the quiz for five successive rounds were 25, – 5, – 10, 10, and 15 so, what was his total at the end?

Jack’s scores in the five successive rounds are 25, -5, -10, 15 and 10

Hence, Their total score of Jack at the end will be = 25 + (-5) + (-10) + 15 + 10

= 25 – 5 – 10 + 15 + 10

∴ Now, Jack’s total score at the end is 35.

Question 4. In the city of Srinagar, temperature was – 5°C on Monday, and then it dropped by two °C on Tuesday. What was the temperature of the city of Srinagar on Tuesday? On Wednesday, the temperature rose by 4°C. What was the temperature on this day?

The temperature on Monday at Srinagar is = -5C

The temperature on Tuesday at the city of Srinagar is dropped by 2C = Temperature on Monday – 2C

= -7 celsius

The temperature on Wednesday at the city Srinagar rose by 4C = Temperature on Tuesday + 4C.

= -3 celsius

Thus, the temperature on days Tuesday and Wednesday was found to be -7C and -3C, respectively.

Question 5. In a magic square, every row, column and diagonal has the same sum. Check which of these following is a magic square. 

Firstly we consider the square (i)

Now By adding these numbers in each of the rows, we get,

= 5 + (- 1) + (- 4) equals to 5 – 1 – 4 = 5 – 5 = 0

= -5 + (-2) + 7 equals to – 5 – 2 + 7 = -7 + 7 = 0

= 0 + 3 + (-3) = 3 – 3 = 0

By adding these numbers in every column we receive,

= 5 + (- 5) + 0 is equal to 5 – 5 = 0

= (-1) + (-2) + 3 equals to -1 – 2 + 3 = -3 + 3 = 0

= -4 + 7 + (-3) equals to -4 + 7 – 3 = -7 + 7 = 0

By adding these numbers in diagonals, we receive,

= 5 + (-2) + (-3) is equal to 5 – 2 – 3 = 5 – 5 = 0

= -4 + (-2) + 0 is equal to – 4 – 2 = -6

Because the sum of one diagonal is not always equal to zero,

Hence, (i) is not a magic square.

Now, we should consider the square (ii)

By adding these numbers to each rows we receive,

= 1 + (-10) + 0 is equal to 1 – 10 + 0 = -9

= (-4) + (-3) + (-2) equal to -4 – 3 – 2 = -9

= (-6) + 4 + (-7) becomes equal to -6 + 4 – 7 = -13 + 4 = -9

By adding these numbers in each column we receive,

= 1 + (-4) + (-6) equals to 1 – 4 – 6 = 1 – 10 = -9

= (-10) + (-3) + 4 equals to -10 – 3 + 4 = -13 + 4

= 0 + (-2) + (-7) equals to 0 – 2 – 7 = -9

= 1 + (-3) + (-7) equals to 1 – 3 – 7 = 1 – 10 = -9

= 0 + (-3) + (-6) equal to 0 – 3 – 6 = -9

Hence This (ii) square is a magic square because the sum of each row, each column and the diagonal becomes equal to -9 (negative).

Question 6. Verify a – (– b) is equal to a + b for the following values of alphabets a and b.

(i) a = 21, b = 18

a = 21 and b = 18

So To verify a – (- b) is equal to a + b

Let us take the Left Hand Side (LHS) = a – (- b)

= 21 – (- 18)

Now, lets take Right Hand Side (RHS) = a + b

By comparing both the LHS and the RHS.

Hence, the value of a and b are verified.

(ii) a = 118, b = 125

a = 118 and b = 125

To verify this a – (- b) = a + b

= 118 – (- 125)

= 118 + 125

Now, take the Right Hand Side (RHS) = a + b

By comparing both the LHS and the RHS

Hence, the values of a and b are verified.

(iii) a = 75, b = 84

a = 75 and b = 84

To verify that the a – (- b) = a + b

= 75 – (- 84)

Now, the Right Hand Side (RHS) = a + b

By comparing both LHS and RHS, we find that,

Hence, the value of a and b is verified as.

(iv) a = 28, b = 11

a = 28 and b = 11

To verify that a – (- b) = a + b

Let us now take Left Hand Side (LHS) = a – (- b)

= 28 – (- 11)

Now, Right Hand Side (RHS) = a + b

Question 7 . A water tank has stepped inside it. A monkey is sitting on the utter topmost step (which is the first step). The water level is present at the ninth step.

(i) He jumps three steps down the stairs and then successively jumps back two steps upwards. In how many jumps will the Monkey reach the following water level?

Let us consider the steps moved down are represented by a positive integer, and then the steps moved up are represented by a negative integer.

Initially, the Monkey is sitting on the topmost step, which is the first step.

In the 1st jump monkey will be at the step = 1 + 3 = 4 steps

In the 2nd jump monkey will be at the step = 4 + (-2) = 4 – 2 = 2 steps

In the 3rd jump monkey will be at the step = 2 + 3 = 5 steps

In the 4th jump monkey will be at the step = 5 + (-2) = 5 – 2 = 3 steps

In the 5th jump monkey will be at the step = 3 + 3 = 6 steps

In the 6th jump monkey will be at the step = 6 + (-2) = 6 – 2 = 4 steps

In the 7th jump monkey will be at the step = 4 + 3 = 7 steps

In the 8th jump monkey will be at the step = 7 + (-2) = 7 – 2 = 5 steps

In the 9th jump monkey will be at the step = 5 + 3 = 8 steps

In the 10th jump monkey will be at the step = 8 + (-2) = 8 – 2 = 6 steps

In the 11th jump monkey will be at the step = 6 + 3 = 9 steps

∴Monkey took a total of 11 jumps (i.e., 9th step) to reach the water level.

(ii) After drinking water, the Monkey wants to go back. For this, the Monkey jumps four steps up and then successively jumps back two steps down in his every move. In how many total jumps will he reach back to the top step?

Let us consider the steps moved down are represented by the positive integers, and then the steps moved up are represented by the negative integers.

Initially, the Monkey is sitting on the ninth step, i.e., at the water level.

In the 1st jump monkey will be at the step = 9 + (-4) = 9 – 4 = 5 steps

In the 2nd jump monkey will be at the step = 5 + 2 = 7 steps

In the 3rd jump monkey will be at the step = 7 + (-4) = 7 – 4 = 3 steps

In the 4th jump monkey will be at the step = 3 + 2 = 5 steps

In the 5th jump monkey will be at the step = 5 + (-4) = 5 – 4 = 1 step

∴ Hence the Monkey took five jumps to reach back to the top step, i.e., the first step.

Question 8. Fill in the blanks to make the following statements true:

(i) (–5) + (– 8) = (– 8) + (…………)

Let us assume that the missing integer is x,

= (–5) + (– 8) which equals to (– 8) + (x)

= – 5 – 8 = – 8 + x

= – 13 = – 8 + x

By sending – 8 from the RHS to the LHS, it becomes 8,

= – 13 + 8 = x

Now substitute the x value in the place of the blank place present,

(–5) + (– 8) = (– 8) + (- 5) … [This following equation is present in the form of the Commutative law of Addition]

(ii) –53 + ………… = –53

= –53 + x = –53

By sending – 53 from the LHS to the RHS, it becomes 53,

= x = -53 + 53

Now substitute the following x value in the blank place,

= –53 + 0 = –53 … [This equation is present in the form of Closure property of Addition]

(iii) 17 + ………… = 0

= 17 + x = 0

By sending 17 from the LHS to the RHS, it becomes -17,

= x = 0 – 17

Now substitute this x value in the blank place,

= 17 + (-17) = 0 … [This equation is present in the form of Closure property of Addition]

= 17 – 17 = 0

(iv) [13 + (– 12)] + (…………) = 13 + [(–12) + (–7)]

= [13 + (– 12)] + (x) = 13 + [(–12) + (–7)]

= [13 – 12] + (x) = 13 + [–12 –7]

= [1] + (x) = 13 + [-19]

= 1 + (x) = 13 – 19

= 1 + (x) = -6

By sending one from the LHS to the RHS, it becomes -1,

= x = -6 – 1

Now substitute the following x value in the blank place value,

= [13 + (– 12)] + (-7) equals to 13 + [(–12) + (–7)] … [This equation is present in the form of the Associative Property of Addition]

(v) (– 4) + [15 + (–3)] equals to [– 4 + 15] +…………

= (– 4) + [15 + (–3)] is equal to [– 4 + 15] + x

= (– 4) + [15 – 3)] equals to [– 4 + 15] + x

= (-4) + [12] = [11] + x

= 8 = 11 + x

Now, By sending 11 from the RHS to the LHS, it becomes -11,

= 8 – 11 = x

Now substitute the x value in the place of the blank place,

= (– 4) + [15 + (–3)] equals to [– 4 + 15] + -3 … [The following equation is in the form of the Associative property of the Addition]

Question 9. Find the product using the suitable properties:

(i) 26 × (– 48) + (– 48) × (–36)

This given equation is in the form of the Distributive law of the  Multiplication property over Addition.

= a × (b + c) becomes equal to (a × b) + (a × c)

Let, a = -48, b = 26, c = -36

= 26 × (– 48) + (– 48) × (–36)

= -48 × (26 + (-36)

= -48 × (26 – 36)

= -48 × (-10)

= 480 … [∵ (- × – = +)

(ii) 8 × 53 × (–125)

The given equation is present in the form of the Commutative law of Multiplication.

= a × b = b × a

= 8 × [53 × (-125)]

= 8 × [(-125) × 53]

= [8 × (-125)] × 53

= [-1000] × 53

(iii) 15 × (–25) × (– 4) × (–10)

This given equation is in the form of the Commutative law of the Multiplication property.

= 15 × [(–25) × (– 4)] × (–10)

= 15 × [100] × (–10)

= 15 × [-1000]

(iv) (– 41) × 102

This given equation is in the form of a Distributive law of the Multiplication property over Addition.

= a × (b + c) = (a × b) + (a × c)

= (-41) × (100 + 2)

= (-41) × 100 + (-41) × 2

= – 4100 – 82

(v) 625 × (–35) + (– 625) × 65

This given equation is in the form of the Distributive law of Multiplication over Addition.

= 625 × [(-35) + (-65)]

= 625 × [-100]

Question 10. A certain freezing process requires that the room temperature be lowered from 40°C at the rate of 5°C every hour. What will be the final room temperature 10 hours after the actual process begins?

Answer 10:-

From the above question, it is given that

Let us take the lowered temperature as a negative integer,

Initial temperature will be= 40oC

Change in temperature per hour is = -5oC

Change in temperature after 10 hours will be = (-5) × 10 = -50oC

∴The final room temperature after the 10 hours of freezing process = 40oC + (-50oC)

Question 11. In a class test containing about ten questions, five marks are awarded for each correct answer and (–2) marks are awarded for every incorrect answer and 0 for questions which are not attempted.

(i) Mohan gets four correct answers and six incorrect answers on his test. What is his total score?

Marks awarded for one correct answer is = 5

The total marks awarded for his four correct answers are = four × 5 = 20 marks.

Marks awarded for 1 wrong answer = -2 (negative)

Total marks awarded for 6 wrong answers is = 6 × -2 = -12

∴Total score obtained by Mohan = 20 + (-12)

(ii) Reshma gets five correct answers and similarly five incorrect answers; what is her total score?

Total marks awarded for 5 correct answer becomes = 5 × 5 = 25

Marks awarded for one wrong answer is = -2

Total marks awarded for 5 wrong answer becomes = 5 × -2 = -10

∴Total score obtained by Reshma is = 25 + (-10)

(iii) Heena gets two correct answers and five incorrect answers out of the seven questions she attempts. What is her final score?

Total marks awarded for 2 correct answer is = 2 × 5 = 10

Marks awarded for the questions which are not attempted is = 0

∴Total score obtained by Heena is = 10 + (-10)

Question 12. A cement company earns a profit of around ₹ 8 per bag of white cement that is sold and simultaneously a loss of ₹ 5 per bag of grey cement that is sold.

(i) The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?

We denote profit by a positive integer and loss by a negative integer,

So From the above question,

The Cement company earns a profit on selling one bag of white cement = ₹ 8 per bag.

The cement company earns a total profit on selling 3000 bags of white cement = 3000 × ₹ 8

And also the, 

Loss on selling one bag of grey cement is = – ₹ 5 per bag.

Loss on selling the 5000 bags of the grey cement = 5000 × – ₹ 5

= – ₹ 25000

Total loss or profit earned by these cement companies is = profit + loss.

= 24000 + (-25000)

Hence, a loss of ₹ 1000 will be incurred by the company.

(ii) What is the number of white cement bags that must sell to have neither a profit nor loss if the total number of grey bags sold is 6,400 bags?

We denote the profit as a positive integer and the loss as a negative integer,

The cement company earns the profit on selling one bag of white cement as = ₹ 8 per bag.

Now Let the number of white cement bags present be x.

The cement company earns a profit on selling these x bags of white cement as = (x) × ₹ 8

Loss on selling one bag of grey cement becomes = – ₹ 5 per bag.

Loss on selling 6400 bags of grey cement becomes = 6400 × – ₹ 5

= – ₹ 32000

According to the above question,

Company to have neither profit nor loss, must sell,

= Profit + loss = 0

= 8x + (-32000) =0

By sending -32000 from the LHS to the RHS, it becomes 32000

= 8x = 32000

= x = 32000/8

Hence, the 4000 bags of white cement should sell to have neither profit nor loss.

Question 13. Evaluate each of the following:

(i) (–30) ÷ 10

= (–30) ÷ 10

When we divide the negative integer by a positive integer, we first divide them as whole numbers and then put the minus sign (-) before the quotient.

(ii) 50 ÷ (–5)

= (50) ÷ (-5)

When we divide the positive integer by a negative integer, we first divide them as whole numbers and then apply the minus sign (-) before the quotient.

(iii) (–36) ÷ (–9)

= (-36) ÷ (-9)

When we divide the negative integer by a similar negative integer, we first divide these as whole numbers and then put the positive sign (+) before the quotient.

(iv) (– 49) ÷ (49)

= (–49) ÷ 49

When we divide the negative integer by a positive integer, we first divide these as whole numbers and then put the minus sign (-) before the quotient.

(e) 13 ÷ [(–2) + 1]

= 13 ÷ [(–2) + 1]

= 13 ÷ (-1)

When we divide the positive integer by a negative integer, we first divide these as whole numbers and then put the minus sign (-) before the quotient.

(f) 0 ÷ (–12)

= 0 ÷ (-12)

When we divide zero by a negative integer, it gives zero.

(g) (–31) ÷ [(–30) + (–1)]

= (–31) ÷ [(–30) + (–1)]

= (-31) ÷ [-30 – 1]

= (-31) ÷ (-31)

When we divide the negative integer by a negative integer, we first divide these as whole numbers and then put the positive sign (+) before the quotient.

(h) [(–36) ÷ 12] ÷ 3

First, we have to solve these integers within the bracket,

= [(–36) ÷ 12]

= (–36) ÷ 12

When we divide a negative integer by a positive integer, we first divide them as whole numbers and then put the minus sign (-) before the quotient.

(i) [(– 6) + 5)] ÷ [(–2) + 1]

The given question can be written as,

= [-1] ÷ [-1]

Question 14. Verify that a ÷ (b + c) is not equal to (a ÷ b) + (a ÷ c) for each of the following symbols of a, b and c.

(i) a = 12, b = – 4, c = 2

From the above question, a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

Given, a = 12, b = – 4 (negative), c = 2

Now, consider that the LHS = a ÷ (b + c)

= 12 ÷ (-4 + 2)

= 12 ÷ (-2)

When we divide a following positive integer by any of the negative integers, we first divide them as a whole number and then put the minus sign (-) before their quotient.

Then, consider that the RHS is equal to = (a ÷ b) + (a ÷ c)

= (12 ÷ (-4)) + (12 ÷ 2)

= (-3) + (6)

By comparing the LHS and RHS, we get,

= LHS ≠ RHS

Hence, the given values have been verified.

(ii) a = (–10), b = 1, c = 1

Given, a = (-10), b = 1, c = 1

= (-10) ÷ (1 + 1)

= (-10) ÷ (2)

When we divide a negative integer by any other positive integer, we first divide them as a whole number and then put the minus sign (-) before the quotient.

Then, consider RHS = (a ÷ b) + (a ÷ c)

= ((-10) ÷ (1)) + ((-10) ÷ 1)

= (-10) + (-10)

By comparing LHS and RHS

Hence, the given values are verified.

Question. Fill in the following blanks:

(a) 369 ÷ _____ = 369

= 369 ÷ x = 369

= x = (369/369)

Hence, put the valve of x in the blank place.

= 369 ÷ 1 = 369

(b) (–75) ÷ _____ = –1

= (-75) ÷ x = -1

= x = (-75/-1)

Now, put the above valve of x in the blank place.

= (-75) ÷ 75 = -1

(c) (–206) ÷ _____ = 1

= (-206) ÷ x = 1

= x = (-206/1)

= (-206) ÷ (-206) = 1

(d) – 87 ÷ _____ = 87

= (-87) ÷ x = 87

= x = (-87)/87

= (-87) ÷ (-1) = 87

(e) _____ ÷ 1 = – 87

= (x) ÷ 1 = -87

= x = (-87) × 1

So, put the valve of x in the blank.

= (-87) ÷ 1 = -87

(f) _____ ÷ 48 = –1

= (x) ÷ 48 = -1

= x = (-1) × 48

Now, put the above valve of x in the following blank.

= (-48) ÷ 48 = -1

Question 15. The temperature at 12 noon was 10 degrees C above zero. If it decreases at the rate of 2C per hour until midnight, at what time would the temperature be eight °C below zero? Also, What would be the temperature at midnight?

From the above question, it is given that,

The temperature at the beginning, which is, at 12 noon, is = 10C

The rate of change of temperature becomes = – 2C per hour.

Temperature present at 1 PM = 10 + (-2) = 10 – 2 = 8° C

Temperature present at 2 PM = 8 + (-2) = 8 – 2 = 6° C

Temperature present at 3 PM = 6 + (-2) = 6 – 2 = 4°C

Temperature present at 4 PM = 4 + (-2) = 4 – 2 = 2°C

Temperature present at 5 PM = 2 + (-2) = 2 – 2 = 0°C

Temperature present at 6 PM = 0 + (-2) = 0 – 2 = -2°C

Temperature present at 7 PM = -2 + (-2) = -2 -2 = -4°C

Temperature present at 8 PM = -4 + (-2) = -4 – 2 = -6°C

Temperature present at 9 PM = -6 + (-2) = -6 – 2 = -8°C

∴At 9 PM, the temperature will be 8° C below zero.

The temperature at mid-night which is at 12 AM

Change in the temperature in every 12 hours = -2°C × 12 = – 24°C

So, at midnight the temperature will be = 10 + (-24)

 At midnight the temperature will be 14°C below 0.

Question 16. In the following class test, (+ 3) marks are given for every correct answer, (–2) marks are given for every the incorrect answer and no marks are given for not attempting any question. 

(i) Radhika scored 20 marks. If she has got around 12 correct answers, then how many questions has she attempted that are incorrect?

(ii) Mohini scores –5 (negative) marks on this test, and though she has got seven correct answers. How many questions has she attempted incorrectly?

Marks awarded for 1 correct answer is = + 3

(i) Radhika, in the test, scored 20 marks

Total marks awarded for every 12 correct answers is = 12 × 3 = 36

Marks awarded for every incorrect answer = Total score – Total marks awarded for 12 correct questions.

So, the number of incorrect answers done by Radhika = (-16) ÷ (-2)

(ii) Mohini scored a total of -5 marks

Total marks awarded for her 7 correct answers is = 7 × 3 = 21

Marks awarded for her incorrect answers = Total score – Total marks awarded for the 12 correct answers.

Hence, the number of incorrect answers made by Mohini = (-26) ÷ (-2)

Question 17. An elevator descends down into a mine shaft at the rate of 6 m per min. If the descent starts from 10 meters above the ground level, how much time will it take to reach – 350 m?

The initial height of the elevator becomes = 10 m

Final depth of elevator is = – 350 m … [the distance descended is denoted by a negative integer]

The total distance to descend by the elevator becomes = (-350) – (10)

Time taken by the elevator to descend (negative) -6 m is = 1 min

So, the total time taken by the elevator to descend – 360 m becomes = (-360) ÷ (-60)

= 60 minutes

= 1 hour Benefits of Solving Important Questions Class 7 Mathematics Chapter 1

Practice is the key to success. The practice habit is very important for students because it will help them in many ways. It will help them to score better in exams. Apart from this, practice will clear doubts, generate interest in the subject matter, and strengthen the concepts. Thus, students must practice sums regularly to improve their exam preparation. The Important Questions Class 7 Mathematics Chapter 1 will help students in many ways. These are-

• The experts have collated the questions from various sources. They have accumulated the questions from the textbook exercises, CBSE sample papers, CBSE past years’ question papers and important reference books. Thus, students will find all the vital questions In this article, and they can solve the questions regularly. Thus, students don’t have to search for questions in different books, but they will find them here. Thus, Chapter 1, Class 7 Mathematics Important Questions includes all the important concepts.
• The experts have not only collated the questions but also provided the solutions. They have given a step-by-step solution for each chapter to help students. Experienced professionals have further checked the answers. Thus, we have ensured the best quality of content for the students. They can follow the solutions and check their answers with the experts’ answers. So, the Mathematics Class 7 Chapter 1 Important Questions will help students to clarify their doubts, boost their confidence and build their concepts. 
• The subject matter experts of Extramarks understand the student’s needs. They have built the question series to help students with their exam preparation. They have collected all the vital questions so students can find them in a single article. Sometimes, students need more than the textbook. Hence, they can follow the Class 7 Mathematics Chapter 1 Important Questions because they will find chapter-wise questions for each subject. Regular practice will strengthen their ideas, and they can solve any question that comes in exams. Thus, the question series will help them to score better in exams.

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Q.1 Which one of the following statements is false?

1. For any two positive integers a and b, a ÷ (–b) = – a ÷ b, where b ≠ 0.

2. The commutativity, associativity and distributivity of integers help to make calculations simpler.

3. The product of three integers does not depend upon the grouping of integers.

4. Division is closed for integers.

Option 4. Explanation

Division is not closed for integers. For example: 2 ÷ 6 =

is not an integer.

Q.2 Which one of the following is false?

Marks: 1 1. Sum of integers a and b is an integer.

2. a + b = b + a, for all integers a and b

3. a – b = b – a, for all integers a and b

4.  a + (b + c) = (a + b) + c, for all integers a, b and c

Ans Option3 Explanation

a – b = b – a, for all integers a and b is false. For example, 2 – 4 = – 2 and 4 – 2 = 2 Thus, 2 – 4 ≠ 4 – 2

Q.3 What is the difference between a temperature of 7º C above zero and a temperature of 3º C below zero?

Ans Option 1. Explanation

Difference between a temperature of 7º C above zero and a temperature of 3º C below zero = 7º C – (– 3º C) = 7º C + 3º C = 10º C

Q.4 A plane is flying at the height of 8750 m above sea level. At a particular point, it is exactly above a submarine floating 1340 m below sea level. What is the vertical distance between them?

Marks: 2 Ans

Height of the plane above sea level = 8750 m Distance of submarine below sea level = – 1340 m Vertical distance = 8750 m – (– 1340 m) = 8750 m + 1340 m = 10,090 m

Q.5 A man walks 22 m towards east and then 17 m towards west. The position of the man with respect to his starting point is ______________.

1.5 m towards west

2.5 m towards east

3.39 m towards east

4.39 m towards west

Ans Option 2. Explanation

Let 22 m towards east be represented by +22, then –17 m represents 17 m towards west. On adding, +22 – 17 = +5 (positive) The position of the man with respect to his starting point = 5 m towards east

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Faqs (frequently asked questions), 1. is class 7 mathematics chapter 1 easy.

Class 7 Mathematics Chapter 1 under CBSE curriculum is about integers. Students will study the properties of integers, how to add and multiply integers and how to put them on the number line. The concepts may be new to them, but they have studied integers in Class 6. They can easily understand the concepts if they follow the textbook seriously. The chapter is relatively easy. Students can take help from the Important Questions Class 7 Mathematics Chapter 1 to solve questions from the chapter.

2. How can the Important Questions Class 7 Mathematics Chapter 1 help students?

The experts of Extramarks have made the question series after taking help from several sources. They have collated the questions from the textbook exercise, CBSE sample papers, important reference books and NCERT exemplar. They have included questions from CBSE past years’ question papers too. Apart from this, they have solved the questions for students, and experienced professionals have further checked the answers. Thus, the Important Questions Class 7 Mathematics Chapter 1 will help the students to practice the sums regularly. It will boost their confidence and increase their marks in exams.

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NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

Integers Class 7 Extra Questions Maths Chapter 1

June 11, 2019 by Sastry CBSE

Extra Questions for Class 7 Maths Chapter 1 Integers

Integers Class 7 Extra Questions Very Short Answer Type

Question 1. Fill in the blanks using < or >. (a) -3 …… -4 (b) 6 ……. -20 (c) -8 …… -2 (d) 5 …… -7 Solution: (a) -3 > -4 (b) 6 > -20 (c) -8 < -2 (d) 5 > -7

Question 2. Solve the following: (i) (-8) × (-5) + (-6) (ii) [(-6) × (-3)] + (-4) (iii) (-10) × [(-13) + (-10)] (iv) (-5) × [(-6) + 5] Solution: (i) (-8) × (-5) + (-6) = (-) × (-) × [8 × 5] + (-6) = 40 – 6 = 34

(ii) [(-6) × (-3)] + (-4) = (-) × (-) × [6 × 3] + (-4) = 18 – 4 = 14

(iii) (-10) × [(-13) + (-10)] = (-10) × (-23) = (-) × (-) × [10 × 23] = 230

(iv) (-5) × [(-6) + 5] = (-5) × (-1) = (-) × (-) × 5 × 1 = 5

Question 3. Starting from (-7) × 4, find (-7) × (-3) Solution: (-7) × 4 = -28 (-7) × 3 = -21 = [-28 + 7] (-7) × 2 – -14 = [-21 + 7] (-7) × 1 = -7 = [-14 + 7] (-7) × 0 = 0 = [-7 + 7] (-7) × (-1) = 7 = [0 + 7] (-7) × (-2) = 14 = [7 + 7] (-7) × (-3) = 21 = [14 + 7]

Question 5. Write five pair of integers (m, n ) such that m ÷ n = -3. One of such pair is (-6, 2). Solution: (i) (-3, 1) = (-3) ÷ 1 = -3 (ii) (9, -3) = 9 ÷ (-3) = -3 (iii) (6, -2) = 6 ÷ (-2) = -3 (iv) (-24, 8) = (-24) ÷ 8 = -3 (v) (18, -6) = 18 ÷ (-6) = -3

Integers Class 7 Extra Questions Short Answer Type

Question 6. Solve the following: (i) (-15) × 8 + (-15) × 4 (ii) [32 + 2 × 17 + (-6)] ÷ 15 Solution: (i) (-15) × 8 + (-15) × 4 = (-15) × [8 + 4] = (-15) × 12 = -180

(ii) [32 + 2 × 17 + (-6)] ÷ 15 = [32 + 34 – 6] ÷ 15 = [66 – 6] ÷ 15 = 60 ÷ 15 = 4

Question 7. The sum of two integers is 116. If one of them is -79, find the other integers. Solution: Sum of two integers = 116 One integer = -79 Other integer = Sum of integer – One of integer = 116 – (-79) = 116 + 79 = 195

Question 8. If a = -35, b = 10 cm and c = -5, verify that: (i) a + (b + c) = (a + b) + c (ii) a × (b + c) = a × b + a × c Solution: (i) Given that a = -35, b = 10, c = -5 LHS = a + (b + c) = (-35) + [10 + (-5)] = (-35) + 5 = -30 RHS = (a + b) + c = [(-35) + 10] + (-5) = (-25) + (-5) = -(25 + 5) = -30 LHS = RHS Hence, verified.

(ii) a × (b + c) = a × b + a × c LHS = a × (b + c) = (-35) × [10 + (-5)] = (-35) × 5 = -175 RHS = a × b + a × c = (-35) × 10 + (-35) × (-5) = -350 + (-) × (-) × (35 × 5) = -350 + 175 = -175 LHS = RHS Hence, verified.

Question 9. Write down a pair of integers whose (i) sum is -5 (ii) difference is -7 (iii) difference is -1 (iv) sum is 0 Solution: (i) (-2) + (-3) = -5 Hence, the required pair of integers = (-2, -3) (ii) -10 – (-3) = -10 + 3 = -7 Hence, the required pair of integers = (-10, -3) (iii) (-3) – (-2) = -1 Hence, the required pair of integers = (-3, -2) (iv) (-4) + (4) = 0 Hence, the required pair of integers = (-4, 4)

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Case Based Questions (MCQ)

• MCQs from NCERT Exemplar
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• Euclid's Division Algorithm
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Question 1 - Case Based Questions (MCQ) - Chapter 1 Class 10 Real Numbers

Last updated at April 16, 2024 by Teachoo

To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.

What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B? (a) 144   (b) 128   (c) 288  (d) 272

If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32 , 36) is (a) 2  (b) 4   (c) 6  (d) 8

36 can be expressed as a product of it’s primes as (a) 2 2   × 3 2   (b) 2 1 × 3 3    (c) 2 3 × 3 1   (d) 2 0 × 3 0

7 × 11 × 13 × 15 + 15 is a (a) Prime number  (b) Composite Number  (c) Neither prime nor composite  (d) None of the above

If p and q are positive integers such that p = ab 2 and q = a 2 b, where a, b are prime numbers, then the LCM (p, q) is (a) ab  (b) a 2 b 2 (c) a 3 b 2 (d) a 3 b 3

Question To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.Question 1 What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B? (a) 144 (b) 128 (c) 288 (d) 272 Minimum Number of books will be the LCM of 32 and 36 LCM = 2 . 2 . 2 . 2 . 2 . 3. 3 = 288 So, correct answer is (C) Question 2 If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32 , 36) is (a) 2 (b) 4 (c) 6 (d) 8 Given that Product of two numbers = HCF × LCM Putting two numbers as 32, 36 and their LCM as 288 32 × 36 = HCF × 288 (32 × 36)/288 = HCF HCF = (32 × 36)/288 HCF = 36/9 = 4 So, correct answer is (B) Question 3 36 can be expressed as a product of it’s primes as (a) 2^2 × 3^2 (b) 2^1 × 3^3 (c) 2^3 × 3^1 (d) 2^0 × 3^0 Doing Prime Factorisation of 36 36 = 2 . 2 . 3 . 3 = 22 × 32 So, correct answer is (A) Question 4 7 × 11 × 13 × 15 + 15 is a (a) Prime number (b) Composite Number (c) Neither prime nor composite (d) None of the above 7 × 11 × 13 × 15 + 15 = 15 × (7 × 11 × 13 + 1) Since the number is divisible by a number other than itself and 1 It is a composite number So, correct answer is (B) Question 5 If p and q are positive integers such that 〖𝑝=𝑎𝑏〗^2 and 𝑞=𝑎^2 𝑏, where a, b are prime numbers, then the LCM (p, q) is (a) ab (b) 𝑎^2 𝑏^2 (c) 𝑎^3 𝑏^2 (d) 𝑎^3 𝑏^3 Finding LCM of ab2 and a2b LCM = a . a . b . b = a2b2 So, correct answer is (A)

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• NCERT Exemplar
• NCERT Exemplar Class 7
• Class 7 Maths
• Class 7 Maths Chapter 1

NCERT Exemplar Solutions for Class 7 Maths Chapter 1 Integers

NCERT Exemplar Solutions for Class 7 Maths Chapter 1 Integers are the best study materials for students who find difficulties in solving problems. These solutions can help students clear doubts quickly and help in understanding topics effectively. Our subject experts formulate these exercises to assist you with your exam preparation to attain good marks in the subject. Students can score good marks in Maths by practising NCERT Exemplar Solutions for Class 7 Maths.

Chapter 1 – Integers solutions are available for download in PDF format, which provides answers to all questions in the NCERT Exemplar Class 7 Maths textbook. An integer is a whole number that can be positive, negative or zero. Positive integers are used in many ways in our daily lives. One such instance is highway numbers, along with roadway speed limits. Negative integers are used in thermometer readings, keeping scores in some games, etc. Now, let us have a look at some of the concepts discussed in this chapter.

• Representation of integers on the number line and their addition and subtraction.
• Properties of addition and subtraction of integers
• Multiplication of integers
• Multiplication of a positive and negative integer
• Division of a positive and negative integer

Download the PDF of NCERT Exemplar Solutions for Class 7 Maths Chapter 1 Integers

Access Answers to Maths NCERT Exemplar Solutions for Class 7 Chapter 1 Integers

Exercise Page No: 8

In the Questions 1 to 25, there are four options, out of which only one is correct. Write the correct one.

1. When the integers 10, 0, 5, – 5, – 7 are arranged in descending or ascending order, then find out which of the following integers always remains in the middle of the arrangement.

(a) 0 (b) 5 (c) – 7 (d) – 5

When the given integers are arranged in descending order we have: 10, 5, 0, -5, -7

When the given integers are arranged in an ascending order we have: -7, -5, 0, 5, 10

It’s seen that in both the orders 0 always remains in the middle of the arrangement.

2. By observing the number line (Fig. 1.2), state which of the following statements is not true.

(a) B is greater than –10 (b) A is greater than 0

(c) B is greater than A (d) B is smaller than 0

(c) B is greater than A.

Since, B lies to the left of zero and A lies to the right of zero on the number line clearly, A has to be greater than B.

3. By observing the above number line (Fig. 1.2), state which of the following statements is true.

(a) B is 2 (b) A is – 4 (c) B is –13 (d) B is – 4

(d) B is -4

Each division on the number line is 1 unit apart. Then, B is 4 units from the left of zero.

4. Next three consecutive numbers in the pattern 11, 8, 5, 2, –, –, — are

(a) 0, – 3, – 6 (b) – 1, – 5, – 8 (c) – 2, – 5, – 8 (d) – 1, – 4, – 7

(d) -1, -4, -7

In the given sequence of numbers, each number differs by 3 from the previous number.

5. The next number in the pattern – 62, – 37, – 12 _________ is

(a) 25 (b) 13 (c) 0 (d) –13

It’s found that the pattern is -62 + 25 = -37, -37 + 25 = -12

So, similarly -12 + 25 = 13

6. Which of the following statements is not true?

(a) When two positive integers are added, we always get a positive integer.

(b) When two negative integers are added we always get a negative integer.

(c) When a positive integer and a negative integer is added we always get a negative integer.

(d) Additive inverse of an integer 2 is (– 2) and additive inverse of (– 2) is 2.

The above statement is false as when a positive and a negative integer is added we may get a positive number or even zero.

7. On the following number line value ‘Zero’ is shown by the point

(a) X (b) Y (c) Z (d) W

It’s observed that each division on the number line is 5 units. So, from 10 taking two division to its left we get zero.

8. If ⊗, O, and • represent some integers on number line, then descending order of these numbers is

The descending order of these numbers is as in option (c).

9. On the number line, the value of (–3) × 3 lies on right hand side of

(a) – 10 (b) – 4 (c) 0 (d) 9

As (-3) x 3 = -9

So, -9 lies to the right to -10.

10. The value of 5 ÷ (–1) does not lie between

(a) 0 and – 10 (b) 0 and 10 (c) – 4 and – 15 (d) – 6 and 6

(b) 0 and 10

The value of 5 ÷ (–1) = -5

As it is a negative number it doesn’t lie between 0 and 10.

11. Water level in a well was 20m below ground level. During rainy season, rain water collected in different water tanks was drained into the well and the water level rises 5 m above the previous level. The wall of the well is 1m 20 cm high and a pulley is fixed at a height of 80 cm. Raghu wants to draw water from the well. The minimum length of the rope that he can use is

(a) 17 m (b) 18 m (c) 96 m (d) 97 m

Height of the wall of the well = 1m 20 cm = 1.2 m

Height of the fixed pulley = 80 cm = 0.8 m

Initially water was available at a depth of 20 m below ground level.

Later, due to rain the water level was raised by 5 m.

Hence, the new depth at which water is available = 20 – 5 = 15 m

The minimum length of the rope required to draw water from the well will be

(1.2 + 0.8 + 15) m = 17 m

12. (– 11) × 7 is not equal to

(a) 11 × (– 7) (b) – (11 × 7) (c) (– 11) × (– 7) (d) 7 × (– 11)

(c) (– 11) × (– 7)

11 x (-7) = -77

– (11 x 7) = -77 and

7 x (-11) = -77

But, (-11) x (-7) = 77

13. (– 10) × (– 5) + (– 7) is equal to

(a) – 57 (b) 57 (c) – 43 (d) 43

Using BODMAS rule,

(-10) x (-5) + (-7) = 50 – 7 = 43

14. Which of the following is not the additive inverse of a?

(a) – (– a) (b) a × (– 1) (c) – a (d) a ÷ (–1)

The additive inverse of a is – a

But, – (-a) = a

15. Which of the following is the multiplicative identity for an integer a?

(a) a (b) 1 (c) 0 (d) – 1

16. [(– 8) × (– 3)] × (– 4) is not equal to

(a) (– 8) × [(– 3) × (– 4)] (b) [(– 8) × (– 4)] × (– 3)

(c) [(– 3) × (– 8)] × (– 4) (d) (– 8) × (– 3) – (– 8) × (– 4)

(d) (– 8) × (– 3) – (– 8) × (– 4)

= [(– 8) × (– 4)] × (– 3)

= [(– 3) × (– 8)] × (– 4)

But, [(– 8) × (– 3)] × (– 4) ≠ (– 8) × (– 3) – (-8) × (– 4)

17. (– 25) × [6 + 4] is not same as

(a) (– 25) × 10 (b) (– 25) × 6 + (– 25) × 4 (c) (– 25) × 6 × 4 (d) – 250

(c) (– 25) × 6 × 4

= (– 25) × 10

= (– 25) × 6 + (– 25) × 4

But, (– 25) × [6 + 4] ≠ (– 25) × 6 × 4

18. – 35 × 107 is not same as

(a) – 35 × (100 + 7) (b) (– 35) × 7 + ( – 35) × 100

(c) – 35 × 7 + 100 (d) (– 30 – 5) × 107

(c) – 35 × 7 + 100

– 35 × 107 = (– 30 – 5) × 107 = – 35 × (100 + 7) = (– 35) × 7 + ( – 35) × 100

But, – 35 × 107 ≠ – 35 × 7 + 100

19. (– 43) × (– 99) + 43 is equal to

(a) 4300 (b) – 4300 (c) 4257 (d) – 4214

By BODMAS rule,

(– 43) × (– 99) + 43 = [(– 43) × (– 99)] + 43 = 4257 + 43 = 4300

20. (– 16) ÷ 4 is not same as

(a) ( – 4) ÷ 16 (b) – ( 16 ÷ 4) (c) 16 ÷ (– 4) (d) – 4

(a) ( – 4) ÷ 16

(– 16) ÷ 4 = -4

But, ( – 4) ÷ 16 = -1/4

21. Which of the following does not represent an integer?

(a) 0 ÷ (– 7) (b) 20 ÷ (– 4) (c) (– 9) ÷ 3 (d) (– 12) ÷ 5

(d) (– 12) ÷ 5

0 ÷ (– 7) = 0, an integer

20 ÷ (– 4) = -5, an integer

(– 9) ÷ 3 = -3, an integer

But, (– 12) ÷ 5 = -2.4, which is a decimal and not an integer

22. Which of the following is different from the others?

(a) 20 + (–25) (b) (– 37) – (– 32) (c) (– 5) × (–1) (d) ( 45 ) ÷ (– 9)

(c) (– 5) × (–1)

As all the remaining options give a value of -5

20 + (–25) = (– 37) – (– 32) = ( 45 ) ÷ (– 9) = -5

But, (– 5) × (–1) = 5

23. Which of the following shows the maximum rise in temperature?

(a) 23° to 32° (b) – 10° to + 1° (c) – 18° to – 11° (d) – 5° to 5°

(b) – 10° to + 1°

As the difference in the temperature = 1° – (10°) = 11° (maximum)

23° to 32° = 32° – 23° = 9°

– 18° to – 11° = -11° – (-18)° = 7°

– 5° to 5° = 5° – (-5)° = 10°

24. If a and b are two integers, then which of the following may not be an integer?

(a) a + b (b) a – b (c) a × b (d) a ÷ b

If a and b are two integers, then

a + b will always be an integer

a – b will always be an integer

a × b will always be an integer

25. For a non-zero integer a, which of the following is not defined?

(a) a ÷ 0 (b) 0 ÷ a (c) a ÷ 1 (d) 1 ÷ a

a ÷ 0 = a/0 is undefined

Encircle the odd one of the following (Questions 26 to 30).

26. (a) (–3, 3) (b) (–5, 5) (c) (–6, 1) (d) (–8, 8)

(c) (–6, 1)

–6 + 1 = -5

Hence, (–6, 1) is the odd one.

27. (a) (–1, –2) (b) (–5, +2) (c) (–4, +1) (d) (–9, +7)

(d) (–9, +7)

–1 + (–2) = -3

–5 + 2 = -3

–4 + 1 = -3

–9 + 7 = -2

Hence, (–9, +7) is the odd one.

28. (a) (–9) × 5 × 6 × (–3) (b) 9 × (–5) × 6 × (–3)

(c) (–9) × (–5) × (–6) × 3 (d) 9 × (–5) × (–6) × 3

(c) (–9) × (–5) × (–6) × 3

(–9) × 5 × 6 × (–3) = 810

9 × (–5) × 6 × (–3) = 810

(–9) × (–5) × (–6) × 3 = -810

9 × (–5) × (–6) × 3 = 810

Hence, (–9) × (–5) × (–6) × 3 is the odd one.

29. (a) (–100) ÷ 5 (b) (–81) ÷ 9 (c) (–75) ÷ 5 (d) (–32) ÷ 9

(d) (–32) ÷ 9

Since, only (–32) ÷ 9 doesn’t give an integer i.e. -32/9 = -3.5555555556

Hence, (–32) ÷ 9 is the odd one.

30. (a) (–1) × (–1) (b) (–1) × (–1) × (–1)

(c) (–1) × (–1) × (–1) × (–1) (d) (–1) × (–1) × (–1) × (–1) × (–1) × (–1)

(b) (–1) × (–1) × (–1)

(–1) × (–1) = 1

(–1) × (–1) × (–1) × (–1) = 1

(–1) × (–1) × (–1) × (–1) × (–1) × (–1) = 1

But, (–1) × (–1) × (–1) = -1

Hence, (–1) × (–1) × (–1) is the odd one.

In Questions 31 to 71, fill in the blanks to make the statements true.

31. (–a) + b = b + Additive inverse of __________.

(–a) + b = b + (-a)

(–a) + b = b + Additive inverse of (a)

32. ________ ÷ (–10) = 0

0 ÷ (–10) = 0/(-10) = 0

33. (–157) × (–19) + 157 = ___________

(–157) × (–19) + 157 = (2983) + 157 = 3140

34. [(–8) + ______ ] + ________ = ________ + [(–3) + ________ ] = –3

-3, 8, -8, 8:

35. On the following number line, (–4) × 3 is represented by the point _________.

(-4) x 3 = -12

Each division on the number line is 2 units. So, D represent -12

36. If x, y and z are integers then (x +___ ) + z = _____ + (y + _____ )

By associative property of integers, we have

(x + y) + z = x + (y + z)

37. (– 43) + _____ = – 43

(– 43) + 0 = – 43

38. (– 8) + (– 8) + (– 8) = _____ × (– 8)

(– 8) + (– 8) + (– 8) = -24 = 3 × (– 8)

39. 11 × (– 5) = – ( _____ × _____ ) = _____

11, 5, -55:

11 × (– 5) = – (11 × 5 ) = -55

40. (– 9) × 20 = _____

(– 9) × 20 = -180

41. (– 23) × (42) = (– 42) × _____

(– 23) × (42) = (– 42) × 23 = 966

42. While multiplying a positive integer and a negative integer, we multiply them as ________ numbers and put a ________ sign before the product.

whole, negative

43. If we multiply ________ number of negative integers, then the resulting integer is positive.

44. If we multiply six negative integers and six positive integers, then the resulting integer is _______

positive integer

When even number of negative integers are multiplied the resulting integer is positive and when six positive integers are multiplied the resulting integer is also a positive.

45. If we multiply five positive integers and one negative integer, then the resulting integer is _______.

When odd number of negative integers are multiplied the resulting integer is negative. Also, when a negative and positive integer are multiplied the resulting integer is negative.

46. _______ is the multiplicative identity for integers.

1 is the multiplicative identity for integers.

i.e. 1 x a = a

47. We get additive inverse of an integer a when we multiply it by _________.

a x (-1) = -a = additive inverse of (a)

48. ( – 25) × ( – 2) =

( – 25) × ( – 2) = 25 x 2 = 50

49. (– 5) × ( – 6) × ( – 7) =

(– 5) × ( – 6) × ( – 7) = – (5 × 6 × 7) = -210

50. 3 × ( – 1) × ( – 15) =

3 × ( – 1 ) × ( – 15) = (-3) x (-15) = 45

51. [12 × ( – 7)] × 5 = ___ × [(– 7) × ___ ]

52. 23 × ( – 99) = ___ × ( – 100 + ___ ) = 23 × ___ + 23 × ___

23, 1, -100, 1:

23 × ( – 99) = 23 × ( – 100 + 1 ) = 23 × (-100) + 23 × 1 (Distributive property of integers)

53. ___ × ( – 1) = – 35

35 × ( – 1) = – 35

54. ____ × ( – 1) = 47

-47 × ( – 1) = 47 (product of even number of negative integers is a positive integer)

55. 88 × ___ = – 88

88 × -1 = – 88

56. ___ × (–93) = 93

-1 × (–93) = 93

57. ( – 40) × __ = 80

( – 40) × (-2) = 80

58. ___ × (–23) = – 920

40 × (–23) = – 920

59. When we divide a negative integer by a positive integer, we divide them as whole numbers and put a ______ sign before quotient.

60. When –16 is divided by _________ the quotient is 4.

Let -16 be divided by x and the quotient is 4

So, -16/x = 4

61. Division is the inverse operation of ____________

Multiplication

62. 65 ÷ ( – 13) =

65 ÷ (– 13) = 65/ (-13) = -5

63. ( – 100) ÷ ( – 10) =

( – 100) ÷ ( – 10) = ( – 100)/ ( – 10) = 10

64. ( – 225) ÷ 5 =

( – 225) ÷ 5 = -45

65. _____÷ ( – 1 ) = – 83

83 ÷ ( – 1 ) = – 83

66. _____ ÷ ( – 1) = 75

(-75) ÷ ( – 1) = 75

67. 51 ÷ _____ = – 51

51 ÷ (-1) = – 51

68. 113 ÷ _____ = – 1

113 ÷ (-113) = – 1

69. (– 95) ÷ _____ = 95

(– 95) ÷ (-1) = 95

70. ( – 69) ÷ ( 69) = _____

( – 69) ÷ ( 69) = (-69)/ 69 = -1

71. ( – 28) ÷ ( – 28) = _____

( – 28) ÷ ( – 28) = (-28)/ (-28) = 1

In Questions 72 to 83, state whether the statements are True or False.

72. 5 – ( – 8) is same as 5 + 8.

5 – ( – 8) = 5 + 8

73. (– 9) + (– 11) is greater than (– 9) – ( – 11).

(– 9) + (– 11) = – 19

But, (– 9) – ( – 11) = – 9 + 11 = 2

So, -19 < 2

Hence, (– 9) + (– 11) < (– 9) – ( – 11)

74. Sum of two negative integers always gives a number smaller than both the integers.

-4 + (-5) = -9

-4 > -9 and -5 > -9

75. Difference of two negative integers cannot be a positive integer.

E.g.: -2 – (-5) = -2 + 5 = 3 (positive integer)

76. We can write a pair of integers whose sum is not an integer.

Sum of two integers is always an integer.

77. Integers are closed under subtraction.

The difference of two integers is always an integer.

78. (– 23) + 47 is same as 47 + (– 23).

In case of addition even if the orders of integers are changed, as the values are equal both are equal.

(– 23) + 47 = 24 and 47 + (– 23) = 24

79. When we change the order of integers, their sum remains the same.

80. When we change the order of integers their difference remains the same.

E.g., 4 – 5 – 8 = -9

But, 5 – 4 – 8 = -7

81. Going 500 m towards east first and then 200 m back is same as going 200 m towards west first and then going 500 m back.

Considering the originating point to the zero of a number line

In the first scenario: 500 – 200 = 300 m to the right from the starting point (0)

In the second scenario: -200 + 500 = 300 m to the right from the starting point (0)

82. (– 5) × (33) = 5 × (– 33)

(– 5) × (33) = -165 and 5 × (– 33) = -165

83. (– 19) × (– 11) = 19 × 11

As the product of numbers with same signs are equal to the absolute value

(– 19) × (– 11) = 19 × 11 = 209

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Integers - Mathematics (Maths) Class 7 - Class 7 - Notes, Videos & Tests

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7th Class Mathematics Integers Question Bank

Done integers total questions - 41.

question_answer 1) What do we call the set of negative numbers and whole numbers?

A)  Natural numbers done clear

B)  Integers   done clear

C)  Positive numbers done clear

D)  The set of whole numbers. done clear

question_answer 2) Which of the following is the smallest positive integer?

A)  0                             done clear

B)  100 done clear

C)  1                               done clear

D)  9 done clear

question_answer 3) Where are the negative numbers located on a horizontal number line?

A)  On the right of 0 done clear

B)  On the left of 0   done clear

C)  Above 0 done clear

D)  Below 0 done clear

question_answer 4) What is the opposite of earning Rs. 100?

A)  \[+\] Rs. 100      done clear

B)  Profit of Rs. 100 done clear

C)  Gain of Rs. 100 done clear

D)  Spending Rs. 100   done clear

question_answer 5) How is the withdrawal of RS. 200 represented?

A)  Depositing Rs. 200 done clear

B)  \[-\]Rs. 200   done clear

C)  Rs. 200            done clear

D)  \[-200\] done clear

question_answer 6) Which of the following is true with respect to \[-28\] and \[-32\]?

A)  \[-28<-32\]     done clear

B)  \[~-28=-32\] done clear

C)  \[-32>-28\]     done clear

D)  \[-28>-32\]   done clear

question_answer 7) Where do we place the positive numbers on a vertical number line with respect to O?

A)  Above           done clear

B)  On its left side done clear

C)  On its right side  done clear

D)  Below done clear

question_answer 8) What is the representation of 30 km towards the west?

A)  30 km east    done clear

B)  \[-30\] km   done clear

C)  30 km        done clear

D)  30 done clear

question_answer 9) What is the nature of the product of a negative integer by itself, odd number of times?

A)  Positive done clear

B)  Negative   done clear

C)  Non negative done clear

D)  Cannot be determined done clear

question_answer 10) What is the nature of the product of a negative number by itself even number of times?

A)  Negative      done clear

B)  0 done clear

C)  Positive         done clear

D)  Non-negative done clear

question_answer 11) A Calculate \[(-32)\times (-4)\times (-3)\times 0\times (-6)\]

A)  27648         done clear

B)  276480 done clear

C)  0               done clear

D)  \[-27648\] done clear

question_answer 12) If the dividend and the divisor have like signs, what is the sign of the quotient?

A)  Positive         done clear

B)  Negative done clear

C)  Zero          done clear

D)  Indeterminate done clear

question_answer 13) If the dividend and divisor have unlike signs, what is the sign of the quotient?

A)  Positive       done clear

A)   \[\left( i \right)-\left( b \right),\left( ii \right)-\left( a \right),\left( iii \right)-\left( c \right),\left( iv \right)-\left( d \right)\] done clear

B)  \[\left( i \right)-\left( a \right),\left( ii \right)-\left( b \right),\left( iii \right)-\left( d \right),\left( iv \right)-\left( c \right)\] done clear

C)  \[\left( i \right)-\left( d \right),\left( ii \right)-\left( c \right),\left( iii \right)-\left( b \right),\left( iv \right)-\left( a \right)\]   done clear

D)  \[\left( i \right)-\left( c \right),\left( ii \right)-\left( d \right),\left( iii \right)-\left( a \right),\left( iv \right)-\left( b \right)\] done clear

question_answer 15) With respect to which of the following operations is closure property satisfied by the set of integers?

A)  \[+,\times \]                     done clear

B)         \[+,\div ,\times \] done clear

C)  \[+,\times ,-\]                    done clear

D)         \[+,-,\div \] done clear

question_answer 16) What is the additive identity for the set of integers?

A)  \[0\]                       done clear

B)         \[(-1)\] done clear

C)  \[1\]                     done clear

D)         \[+10\] done clear

question_answer 17) Which of the following is the multiplicative identity in the set of integers?

A)  \[1\]                       done clear

C)  \[0\]                     done clear

D)         \[(-10)\] done clear

question_answer 18) What is the value of\[124\times 4-3+118\div 2\]?

A)  \[552\]                   done clear

B)         \[496\] done clear

C)  \[553\]                 done clear

D)         \[-553\] done clear

question_answer 19) Which of the following orders is used while evaluating an expression?

A)  \[[\,],\,\,(\,),\,\,\{\,\}\]                done clear

B)         \[\{\,\},\,\,(\,),\,\,[\,]\] done clear

C)  \[(\,),\,\,\{\,\},\,\,[\,]\]                  done clear

D)         \[(\,),\,\,[\,],\,\,\{\,\}\] done clear

question_answer 20) If a negative sign precedes a bracket, what happens to the terms inside it?

A)  Their signs are changed.   done clear

B)  The terms are reciprocated. done clear

C)  The signs remain the same. done clear

D)  The terms are doubled. done clear

question_answer 21) If a positive sign precedes a bracket, what happens to the terms inside it?

A)  Signs of the terms will be changed. done clear

B)  Every term is reciprocated. done clear

C)  Every term will become zero. done clear

D)  No change occurs in any of the terms.   done clear

question_answer 22) What is the value of the expression \[7-[13-\{-2-6(6\,\,of\,\,-5)\}]\]?

A)  \[-172\]               done clear

B)         \[180\] done clear

C)  \[172\]                   done clear

D)         \[0\] done clear

question_answer 23) What is the sign of the product of two integers with like signs?

A)  Negative             done clear

B)         Positive   done clear

C)  0                             done clear

D)         Cannot be determined done clear

question_answer 24) What is the sign of the product of two integers with unlike signs?

A)  Negative   done clear

C)  Positive done clear

question_answer 25) Which of the following operations on integers satisfy the commutative property?

A)  \[-,\,\div \]        done clear

B)         \[-,\,\times \] done clear

C)  \[+,\,-\]                               done clear

D)         \[+,\,\times \]   done clear

question_answer 26) Over which of the following operations is multiplication distributed in the set of integers?

C)  \[+,\,-\]                                 done clear

D)         \[\times ,\,\div \] done clear

question_answer 27) What is the sign of the product obtained when a positive integer is multiplied by \[-1\]?

A)  Positive               done clear

C)  0             done clear

D)  Non negative done clear

question_answer 28) The sum of two integers is 62. If one o1 the integers is \[-48\] what is the other?

A)  \[14\]                   done clear

B)         \[-14\] done clear

C)  \[-110\]               done clear

D)         \[110\]   done clear

question_answer 29) The product of two integers is \[-48\]. If one of the integers is \[-6,\]what is the value of the other?

A)  \[1\]                     done clear

B)         \[288\] done clear

D)         \[8\]   done clear

question_answer 30) A man walked 3 km towards North then 8 km towards South. What is his final position with respect to his initial position?

A)  5 km towards East done clear

B)  3 km towards South done clear

C)  8 km towards North       done clear

D)  5 km towards South   done clear

question_answer 31) What is the smallest negative integer?

A)  \[-1\]                    done clear

B)         \[-10\] done clear

C)  \[0\]                     done clear

D)         Does not exist   done clear

question_answer 32) In a quiz, positive marks were given for correct answers and negative marks for incorrect answers. If Guru's scores in five successive rounds were \[35,-10,-15,\text{ }20\]and 5, what is his total score at the end?

A)  \[25\]                   done clear

B)         \[35\]   done clear

C)  \[45\]                   done clear

D)         \[55\] done clear

question_answer 33) A deep well has steps inside it. A monkey is sitting on the topmost step (i.e., the first step). The water level is at the ninth step. If the monkey jumps 3 steps down and then jumps back 2 steps up, how many jumps does it have to make to reach the water level?

A)  \[11\]                                     done clear

B)         \[9\] done clear

C)  \[7\]                     done clear

D)         \[5\] done clear

question_answer 34) A certain freezing process requires that room temperature be lowered from \[{{4}^{o}}C\]at the rate of \[{{5}^{o}}C\] every hour. What is the room temperature after 10 hours?

A)  \[{{0}^{o}}C\]                   done clear

B)         \[-{{5}^{o}}C\] done clear

C)  \[-{{10}^{o}}C\]                 done clear

D)         \[-{{15}^{o}}C\] done clear

question_answer 35) In a class test containing 10 questions, 3 marks are awarded for every correct answer and \[(-1)\] mark is awarded for every incorrect answer and 0 for the questions not attempted. Srinu gets two correct and six incorrect answers out of eight questions he attempts. What is his total score?

A)  \[0\]       done clear

B)                         \[2\] done clear

C)  \[-2\]   done clear

D)         \[6\] done clear

question_answer 36) What should be multiplied by \[(-12)\] in order to get 180?

A)  \[15\]                                   done clear

B)         \[-15\]   done clear

C)  \[16\]                                   done clear

D)         \[-16\] done clear

question_answer 37) A lift descends into an underground floor at the rate of 6 metres per minute. If the descent starts from 10 metres above the ground level, how much time will it take to descend 350 metres?

A)  30 minutes    done clear

B)  50 minutes done clear

C)  1 hour          done clear

D)  1 hour 30 minutes done clear

question_answer 38) The temperature at 12 noon was \[{{10}^{o}}C\] above zero. If it decreases at the rate of \[{{2}^{o}}C\] per hour until midnight, what would be the temperature at 9 p.m.?

A)  \[-{{8}^{o}}C\]                    done clear

B)         \[-{{6}^{o}}C\] done clear

C)  \[{{8}^{o}}C\]                   done clear

D)         \[{{6}^{o}}C\] done clear

question_answer 39) What is the identity element with respect to subtraction in integers?

A)  \[0\]                       done clear

B)         \[1\] done clear

C)  \[-1\]                    done clear

D)         Does not exist done clear

question_answer 40) Which of the following statements holds correct?

A)  \[N\subset W\subset Z\]       done clear

B)  \[Z\subset N\subset W\] done clear

C)  \[W\subset N\subset Z\] done clear

D)  \[Z\subset W\subset N\] done clear

question_answer 41) The quotient of two numbers is \[(-17)\]. If one of the numbers is \[(-340),\]what is the other number?

A)  \[20\]                     done clear

B)         \[17\]   done clear

C)  \[(-20)\]              done clear

D)         \[(-30)\] done clear

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NCERT Exemplar for Class 7 Maths Solutions Chapter 1 Integers

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Class 7 Maths NCERT Exemplar Solutions Chapter 1- Integers

Free PDF download of NCERT Exemplar for Class 7 Maths Chapter 1 - Integers solved by expert Maths teachers on Vedantu.com as per NCERT (CBSE) Book guidelines. All Chapter 1 - Integers exercise questions with solutions to help you to revise the complete syllabus and score more marks in your examinations.

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Access NCERT Exemplar Solutions for Class 7 Mathematics

Chapter 1 - Integers

(Examples, Easy Methods and Step by Step Solutions)

Solved examples:

1. Madhre is standing in the middle of a bridge which is 20 m above the water level of a river. If a 35 m deep river is flowing under the bridge (see figure), then the vertical distance between the foot of Madhre and bottom level of the river is:

(a) 55 m 

(b) 35 m 

(c) 20 m 

Ans: The correct answer is (a).

Vertical distance $= 20 m + 35 m = 55 m$

2. $\text{[(– 10) × (+ 9)] + (–10)}$ is equal to

(a) 100 

(b) –100 

(c) – 80 

Ans: Correct answer is (b)

$\text{[(– 10) × (+ 9)] + (–10)}$

$= – 90 – 10$

3. $–16 \div \text{[}8 \div (–2)\text{]}$ is equal to

(a) –1 

(b) 1 

(c) 4 

Ans: Correct answer is (c),

$- 16 \div \left[ {8 \div \left( { - 2} \right)} \right] =  - 16 \div \left[ {\dfrac{8}{{ - 2}}} \right]$ 

$=  - 16 \div \left[ { - 4} \right]$ 

$=\dfrac{{ - 16}}{{ - 4}}$ 

$= 4$ 

In questions 4 and 5, fill in the blanks to make the statements true.

4. (– 25) $\times$ 30 = – 30 $\times$ _______.

$(– 25)  \times 30 = – 30  \times 25$

5. $75 ÷ _______ = – 75$

\[75 \div \left( { - 1} \right) =  - 75\]

In questions 6 and 7, state whether the statements are True or False.

6. $(–5)  \times (–7)$ is same as $(–7)  \times (–5)$

$(–5)  \times (–7) = 35$

$(–7)  \times (–5) = 35$

7. $(– 80) \div (4)$ is not same as $80 \div (–4)$

$\left( { - 80} \right) \div \left( 4 \right) = \dfrac{{ - 80}}{4} =  - 20$

$80 \div \left( { - 4} \right) = \dfrac{{80}}{{ - 4}} =  - 20$ 

So, both are the same.

8. Find the odd one out of the four options in the following:

(a) (–2, 24) 

(b) (–3, 10) 

(c) (–4, 12) 

(d) (–6, 8)

Ans: Odd one is (b).

Here $– 2  \times 24 = – 48$,

$– 4  \times 12 = – 48$ and

$– 6  \times 8 = – 48$

All the pairs i.e. (–2, 24); (–4, 12); (–6, 8) give the same answer on multiplication, whereas –3 × 10 = –30, gives a different answer. 

9. Find the odd one out of the four options given below:

(a) (–3, –6) 

(b) (+1, –10) 

(c) (–2, –7) 

(d) (–4, –9)

Ans: Odd one out is (d).

 Here –3 + (–6) = –9,

+1 + (–10) = –9 and

–2 + (–7) = –9

All the above pairs i.e. (–3, –6); (+1, –10); (–2, –7) give the same answer on adding, whereas – 4 + (–9) = –13, gives a different answer. 

10. Match the integer in column I to an integer in column II so that the sum is between –11 and – 4.

Ans: (a) ↔ (iii)

As –6 + (+1) = –5, which lies between –11 and –4.

As +1 + (–11) = –10 which lies between –11 and –4.

As +7 + (–13) = –6 which lies between –11 and –4.

As –2 + (–5) = –7 which lies between –11 and –4.

11. If a is an integer other than 1 and –1, match the following:

Ans: (a) ↔ (iv) 

$a \div \left( { - 1} \right) = \dfrac{a}{{ - 1}} =  - a$

(b) ↔ (iii) 

$1 \div a = \dfrac{1}{a}$

Since a is an integer, $\dfrac{1}{a}$ will not be an integer.

(c) ↔ (ii) 

$\left( { - a} \right) \div \left( { - a} \right) = \dfrac{{ - a}}{{ - a}} = 1$

$\dfrac{a}{{ + 1}} = a$

12. Write a pair of integers whose sum is zero (0) but the difference is 10.

Ans: Since the sum of two integers is zero, one integer is the additive inverse of another integer, like – 3, 3; – 4, 4 etc. 

But the difference has to be 10. So, the integers are 5 and – 5 as $5 – (–5)$ is 10.

13. Write two integers which are smaller than –3, but their difference is greater than –3.

Ans: – 5 and – 4 are smaller than – 3 but their difference is $(–4) – (–5) = 1$ which is greater than – 3.

– 6 and –10 are smaller than – 3 but their difference is $(–6) – (–10) = 4$ which is greater than – 3.

14. Write a pair of integers whose product is – 15 and whose difference is 8.

Ans: There are few pairs of integers whose product is – 15.

e.g.$ – 1 × 15$

$3 × (– 5)$

$15 × (– 1)$

but the difference between –3 and 5 or –5 and 3 is 8. So, the required pair of integers is $– 3, 5$ and $– 5, 3$.

15. If $∆$ is an operation such that for integers a and b we have $a ∆ b = a × a + b × b – a × b$, then find $(–3) ∆ 2.$

Ans: $–3 ∆ 2 = (–3) × (–3) + 2 × 2 – (–3) × 2$ 

$= 9 + 4 – (– 6) = 13 + 6 = 19.$

16: In an objective type test containing 25 questions. A student is to be awarded +5 marks for every correct answer, –5 for every incorrect answer and zero for not writing any answer. Mention the ways of scoring 110 marks by a student.

Ans: Marks scored = +110

So, minimum correct responses $= 110 ÷ (+5) = 22$

Correct responses = 22

Marks for 1 correct response = + 5

Marks for 22 correct response $= +110$ (As 22 × 5 = 110)

Marks scored = +110

Marks obtained for incorrect answer = 0

So, no incorrect response

And, therefore, 3 were un-attempted

Correct responses = 23

Marks from 23 correct responses = + 115 (As 23 × 5 = 115)

Marks scored = + 110

Marks obtained for incorrect answers = 110 – (+115)

Marks for 1 incorrect answer = –5

Number of incorrect responses = (–5) ÷ (–5)

So, 23 correct, 1 incorrect and 1 un-attempted.

Correct responses = 24

Marks from 24 correct responses = + 120 (As 24 × 5 = 120)

Marks obtained for incorrect answers = +110 – (+120)

Number of incorrect responses = (–10) ÷ (–5)

Thus, the number of questions = 24 + 2 = 26. Whereas, the total number of questions is 25. So, this case is not possible.

So, the possible ways are:

• 22 correct, 0 incorrect, 3 un-attempted.

• 23 correct, 1 incorrect, 1 un-attempted.

17. A boy standing on the third stair goes up five more stairs. Which stair is he standing at now? At which step will he be after he comes down 2 stairs?

Ans: He is currently at the third stair i.e. at (+3).

• He goes up 5 stairs in the same direction.

• Since 3 + 5 = 8. Therefore, he is at the 8th stair on the staircase.

Now, the boy comes down 2 stairs. Since he comes down in the opposite direction i.e. downwards by 2 stairs (i.e. –2), so 8 + (–2) = 8 – 2 = 6. 

Therefore, he is at 6th step now.

1. When the integers 10, 0, 5, -5, -7 are arranged in descending or ascending order, then find out which of the following integers always remains in the middle of the arrangement. (a) 0 (b) 5 (c) –7 (d) –5 Ans: Option (a) is correct.

The integers are 10, 0, 5, -5, -7 Descending order: 10, 5, 0, – 5, – 7 Ascending order: -7, – 5, 0, 5, 10 Thus, 0 is the integer which always remains in the middle of the arrangement.

2. By observing the number line, state which of the following statements is not true?

(b) A is greater than 0

(c) B is greater than A

(d) B is smaller than 0 Ans: Option (d) is correct. 

Since B is on the left side of the number line to A, B is smaller than A.

3. By observing the number line, state which of the following statements is true?

(b) A is – 4

(c) B is -13

(d) B is – 4

Ans: Option (d) is correct.

Here, A is 7 and B is -4.

4. Next three consecutive numbers in the pattern 11, 8, 5, 2,______ ,__ ,__ are (a) 0, – 3, – 6 (b)-1,-5,-8 (c) – 2, — 5, – 8 (d) -1,-4,-7 Ans: Option (d) is correct. Here, the pattern is 11 – 3 = 8, 8 – 3 = 5, 5 – 3 = 2 So, the next three consecutive numbers will be 2 – 3 = -1, -1 – 3 = – 4, -4 – 3 = – 7 i.e., -1, -4, -7.

5. The next number in the pattern – 62,- 37,- 12 is_________________ . (a) 25 (b) 13 (c) 0 (d) -13 Ans: Option (b) is correct. Here, the pattern is -62 + 25 = -37,   -37 + 25 = -12 So, next number in the pattern will be -12 + 25 = 13

6. Which of the following statements is not true? (a) When two positive integers are added, we always get a positive integer. (b) When two negative integers are added, we always get a negative integer. (c) When a positive integer and a negative integer are added, we always get a negative integer. (d) Additive inverse of an integer 2 is (-2) and additive inverse of (-2) is 2. Ans: Option (c) is correct. Statement (c) is false because when a positive integer and a negative integer is added we may also get a positive integer or zero. For example, -2 + 2 = 0 and -4 + 5 = 1.

7. On the following number line value, ‘zero’ is shown by the point

(d) W Ans: Option (c) is correct. 

8. If  these following represent some integers on number line

Then descending order of these numbers is

Ans: Option (c) is correct. Descending order of given numbers is 

9. On the number line, the value of (-3) x 3 lies on right hand side of (a) -10 (b) – 4 (c) 0 (d) 9 Ans: Option (a) is correct. Since, (-3) × 3 = – 9 It lies on right hand side of -10.

10. The value of $5 ÷ (- 1)$ does not lie between (a) 0 and -10 (b) 0 and 10 (c) – 4 and -15 (d) – 6 and 6 Ans: Option (b) is correct. The value of $5÷(−1) = −5$ Hence, -5 does not lie between 0 and 10.

11. Water level in a well was 20 m below ground level. During the rainy season, rainwater collected in different water tanks is drained into the well and the water level rises 5 m above the previous level. The wall of the well is 1 m 20cm high and a pulley is fixed at a height of 80 cm. Raghu wants to draw water from the well. The minimum length of the rope, that he can use is

Ans: Option (a) is correct. 

Height of the wall of the well = 1 m 20 cm = 1.20 m Height of the pulley = 80 cm = 0.80 m So, required minimum length of the rope = (20 – 5 + 1.20 + 0.80) m = (15 + 2) m = 17 m

Therefore, the minimum length of the rope is 17 m.

12. (-11) × 7 is not equal to (a) 11 × (-7) (b) -(11 × 7) (c) (- 11) × (- 7) (d) 7 × (-11) Ans: Option (c) is correct.

(-11) × 7 = – (11 × 7) = 11 × (-7) = 7 × (-11) = -77 But (-11) × 7 ≠ (-11) × (-7)             {As (-11) × (-7) = 77}

13. (- 10) × (- 5) + (- 7) is equal to (a) -57 (b) 57 (c) -43 (d) 43 Ans: Option (d) is correct. (-10) × (- 5) + (- 7) = 50 + (-7) = 50 – 7 = 43

14. Which of the following is not the additive inverse of a? (a) – (-a) (b) a × (-1) (c) – a (d) a ÷ (-1) Ans: Option (a) is correct. 

Additive inverse of a is (- a). So, option (b), (c) and (d) equals to -a. Now since –(-a) = a which cannot be the additive inverse of a.

15. Which of the following is the multiplicative identity for an integer a? (a) a (b) 1 (c) 0 (d) -1 Ans: Option (b) is correct.

Multiplicative identity for an integer a is 1. { As a × 1 = a = 1 × a}

16. $\left[(- 8) × (- 3)\right] × (- 4)$ is not equal to (a) (- 8) × $\left[(- 3) × (- 4)\right] $ (b) $\left[(- 8) × (- 4)\right] $ × (- 3) (c) $\left[(- 3) × (- 8)\right] $ × (- 4) (d) (- 8) × (- 3) – (- 8) × (- 4) Ans: Option (d) is correct. 

$\left[(-8) × (-3)\right] $ × (-4) = (-8) × $\left[(-3) × (-4)\right] $ = $\left[(-8) × (-4)\right] $ × (-3) = $\left[(-3) × (-8)\right] $ × (-4) But $\left[(-8) × (-3)\right] $ × (-4) ≠ (-8) ×(-3) – (-8) × (-4)

17. (- 25) × $\left[6 + 4\right]$ is not same as (a) (-25) × 10 (b) (-25) × 6 + (- 25) × 4 (c) -25 × 6 × 4 (d) – 250 Ans: Option (c) is correct. 

(- 25) × $\left[6 + 4\right] $= (-25) × 10

= -250 (- 25) × $\left[6 + 4\right] $= (-25) × 6 + (- 25) × 4

But (- 25) × $\left[6 + 4\right] $ ≠ (- 25) × 6 × 4 

18. – 35 × 107 is not same as (a) – 35 × (100 + 7) (b) (- 35) × 7 + (- 35) × 100 (c) – 35 × 7 + 100 (d) (-30 -5) × 107 Ans: Option (c) is correct. 

– 35 × 107 = – 35 × (100 + 7) = (- 35) × 7 + (- 35) × 100 = (-30 -5) × 107

But – 35 × 107 ≠ -35 × 7 + 100

19. (- 43) × (- 99) + 43 is equal to (a) 4300 (b) – 4300 (c) 425 (d) -4214 Ans: Option (a) is correct. 

(- 43) × (- 99) + 43 = 43× 99 + 43 = 4257 + 43 = 4300

20. $(- 16) ÷ 4$ is not same as (a) $(-4) ÷ 16$ (b) $-(16 ÷ 4)$ (c) $16 ÷ (-4)$ (d) – 4 Ans: Option (a) is correct. 

$\left( { - 16} \right) \div 4 = \dfrac{{ - 16}}{4} =  - 4$ But $\left( { - 4} \right) \div 16 = \dfrac{{ - 4}}{{16}} = \dfrac{{ - 1}}{4}$ So, $(-16) ÷ 4$ is not same as $(-4) ÷ 16.$

21. Which of the following does not represent an integer? (a) 0 ÷ (- 7) (b) 20 ÷ (- 4) (c) (-9) ÷ 3 (d) (-12) ÷ 5 Ans: Option (d) is correct. (a) 0 ÷ (-7) = 0 (b) 20 ÷ (- 4) = -5 (c) (-9) ÷ 3 = -3 (d) (−12) ÷ 5 = $\dfrac{{ - 12}}{5}$ Hence, (-12) ÷ 5 does not represent an integer.

22. Which of the following is different from the others? (a) 20 + (-25) (b) (-37) – (-32) (c) (-5) × (-1) (d) 45 ÷ (- 9) Ans: Option (c) is correct. (a) 20 + (- 25) = 20 – 25 = – 5 (b) (- 37) – (- 32) = – 37 + 32 = – 5 (c) (- 5) × (- 1) = 5 (d) (45) ÷ (−9) = −5 Hence, (-5) × (-1) is different.

23. Which of the following shows the maximum rise in temperature? (a) 23° to 32° (b) -10° to 1° (c) -18° to-11° (d) -5° to 5° Ans: Option (b) is correct.

Rise in temperature, (a) 32° – 23° = 9° (b) 1°- (-10)° = 1° + 10° = 11° (maximum) (c) -11°- (-18)° = -11° + 18° = 7° (d) 5° – (-5°) = 5° + 5° = 10° Hence, the maximum rise in temperature -10° to +1°.

24. If a and b are two integers, then which of the following may not be an integer? (a) a + b (b) a – b (c) a × b (d) a ÷ b Ans: Option (d) is correct. 

If a and b are two integers, then a + b is always an integer. a – bis always an integer. a × b is also an integer, but a ÷ b may or may not be an integer.

25. For a non-zero integer a, which of the following is not defined? (a) a ÷ 0 (b) 0 ÷ a (c) a ÷1 (d) 1 ÷ a Ans: Option (a) is correct. 

\[{\text{a}} \div 0 = \dfrac{{\text{a}}}{0}\] which is not defined.

Directions: Encircle the odd one of the following: (questions 26 to 30)

26. (a) (-3, 3) (b) (-5, 5) (c) (-6, 1) (d) (-8, 8) Ans: Option (c) is correct. 

(a) -3 + 3 = 0 (b) -5 + 5 = 0 (c) -6 + 1 = -5 (d) -8 + 8 = 0 So, (-6,1) is different.

27. (a) (-1, -2) (b) (-5, 2) (c) (- 4, 1) (d) (- 9, 7) Ans: Option (d) is correct. 

(a) -1 – 2 = -3 (b) -5 + 2 = -3 (c) -4 + 1 = -3 (d) -9 + 7 = -2 So, (-9, +7) is different.

(a) (- 9) × 5 × 6 × (- 3) (b) 9 × (-5) × 6 × (-3) (c) (- 9) × (- 5) × (- 6) × 3 (d) 9 × (- 5) × (- 6) × 3 Ans: Option (c) is correct. 

(a) (- 9) × 5 × 6 × (- 3) = 810 (b) 9 × (-5) × 6 × (-3) = 810 (c) (- 9) × (- 5) × (- 6) × 3 = -810 (d) 9 × (- 5) × (- 6) × 3 = 810 So,  (- 9) × (- 5) × (- 6) × 3 is different.

(a) (-100) ÷ 5 (b) (-81) ÷ 9 (c) (- 75) ÷ 5 (d) (-32) ÷ 9 Ans: Option (d) is correct.

(a) $\left( { - 100} \right) \div 5 = \dfrac{{ - 100}}{5} =  - 20$

(b) $\left( { - 81} \right) \div 9 = \dfrac{{ - 81}}{9} =  - 9$

(c) $\left( { - 75} \right) \div 5 = \dfrac{{ - 75}}{5} =  - 15$

(d) $\left( { - 32} \right) \div 9 = \dfrac{{ - 32}}{9}$ Here, -20, -9, -15 all are integers $\dfrac{{ - 32}}{9}$ is not an integer. 

30. (a) \[\left( { - {\text{ }}{\mathbf{1}}} \right){\text{ }} \times {\text{ }}\left( { - {\text{ }}{\mathbf{1}}} \right)\] (b) \[\left( { - {\text{ }}{\mathbf{1}}} \right){\text{ }} \times {\text{ }}\left( { - {\text{ }}{\mathbf{1}}} \right) \times {\text{ }}\left( { - {\text{ }}{\mathbf{1}}} \right)\] (c) \[\left( { - {\text{ }}{\mathbf{1}}} \right){\text{ }} \times {\text{ }}\left( { - {\text{ }}{\mathbf{1}}} \right) \times {\text{ }}\left( { - {\text{ }}{\mathbf{1}}} \right) \times {\text{ }}\left( { - {\text{ }}{\mathbf{1}}} \right)\] (d) \[\left( { - {\text{ }}{\mathbf{1}}} \right){\text{ }} \times {\text{ }}\left( { - {\text{ }}{\mathbf{1}}} \right) \times {\text{ }}\left( { - {\text{ }}{\mathbf{1}}} \right) \times {\text{ }}\left( { - {\text{ }}{\mathbf{1}}} \right) \times {\text{ }}\left( { - {\text{ }}{\mathbf{1}}} \right) \times {\text{ }}\left( { - {\text{ }}{\mathbf{1}}} \right)\] Ans: Option (b) is correct. 

$\left( {\text{a}} \right){\text{ }}\left( { - 1} \right){\text{ }} \times {\text{ }}\left( { - 1} \right){\text{ }} = {\text{ }}1$

$\left( {\text{b}} \right){\text{ }}\left( { - 1} \right){\text{ }} \times {\text{ }}\left( { - 1} \right){\text{ }} \times {\text{ }}\left( { - 1} \right){\text{ }} = {\text{ }} - 1$

$\left( {\text{c}} \right){\text{ }}\left( { - 1} \right){\text{ }} \times {\text{ }}\left( { - 1} \right){\text{ }} \times {\text{ }}\left( { - 1} \right){\text{ }} \times {\text{ }}\left( { - 1} \right){\text{ }} = {\text{ }}1$

$\left( {\text{d}} \right){\text{ }}\left( { - 1} \right){\text{ }} \times {\text{ }}\left( { - 1} \right){\text{ }} \times {\text{ }}\left( { - 1} \right){\text{ }} \times {\text{ }}\left( { - 1} \right){\text{ }} \times {\text{ }}\left( { - 1} \right){\text{ }} \times {\text{ }}\left( { - 1} \right){\text{ }} = {\text{ }}1$ So, \[\left( { - 1} \right){\text{ }} \times {\text{ }}\left( { - 1} \right){\text{ }} \times {\text{ }}\left( { - 1} \right)\] is different.

Directions: In s 31 to 71, fill in the blanks to make the statements true. 31. (- a) + b = b + additive inverse of ___. Ans: a

(-a) + b = b + (-a) = b + additive inverse of a.

32. __________ ÷ (- 10) = 0 Ans: 0

Let the missing number to be x.

$x \div \left( { - 10} \right) = 0$

$\Rightarrow \dfrac{x}{{ - 10}} = 0$

$\Rightarrow x = 0$ 

33. (- 157) × (- 19) + 157 =___________. Ans: 3140

$\left( { - 157} \right){\text{ }} \times {\text{ }}\left( { - 19} \right){\text{ }} + {\text{ }}157{\text{ }} = {\text{ }}157{\text{ }} \times {\text{ }}19{\text{ }} + {\text{ }}157{\text{ }} \times {\text{ }}1$ 

 $={\text{ }}157{\text{ }} \times {\text{ }}\left[ {19{\text{ }} + {\text{ }}1} \right]{\text{ }}$ 

 $={\text{ }}157{\text{ }} \times {\text{ }}20{\text{ }}$ 

 $={\text{ }}3140$ 

34. [(- 8) + ___] + ___ =   ___ + [(-3) + ___] = – 3 Ans: -3, 8, -8, 8 

[(-8) + (-3)] + 8 = -8 + [(-3) + 8] = -3

35. On the following number line, (- 4) × 3 is represented by the point_____ .

-20-(-4) × 2 = – 12

So, D represents -12.

36. If x, y and z are integers, then (x +____) + z =____ + (y +____) Ans: y, x, z 

(x + y) + z = x + (y + z) (Associative property of integers)

37. (-43) + __________ = (-43) Ans: 0

Let the missing number be x.

(-43) + x = – 43

x = -43 + 43 = 0

38. (- 8) + (- 8) + (- 8) =_______ × (- 8) Ans: 3 

$\left( { - 8} \right){\text{ }} + {\text{ }}\left( { - 8} \right){\text{ }} + {\text{ }}\left( { - 8} \right){\text{ }} = {\text{ }}x{\text{ }} \times {\text{ }}\left( { - 8} \right)$ 

$3\left( { - 8} \right) = {\text{ }}x{\text{ }} \times {\text{ }}\left( { - 8} \right){\text{ }}$ 

$x = {\text{ }}3{\text{ }}$ 

39. 11 × (- 5) = – (_____ x____) =_____ Ans: 11, 5, -55

11 × (-5) = -(11 × 5) = -55

40. (- 9) × 20 =_______ Ans: -180 

(-9) × 20 = x

41. (- 23) × (42) = (- 42) ×______ Ans: 23 

(-23) × (42) = (-42) × (23)

42. While multiplying a positive integer and a negative integer, we multiply them as ___ numbers and put a ___   sign before the product. Ans: Whole, negative

43. If we multiply___ number of negative integers, then the resulting integer is positive. Ans: Even

44. If we multiply six negative integers and six positive integers, then the resulting integer is___. Ans: Positive 

When even numbers of negative integers are multiplied, they give positive integers and when positive integers are multiplied, they always give positive integers.

45. If we multiply five positive integers and one negative integer, then the resulting integer is ___. Ans: Negative

When an odd number of negative integers multiplied, they give a negative integer. Also, when a negative and a positive integer are multiplied, they give a negative integer.

46. ________ is the multiplicative identity for integers. Ans: 1 

e.g. if a is an integer then a × 1 = 1 × a = a.

47. We get the additive inverse of an integer a, when we multiply it by ___. Ans: (-1) 

a × (-1) = -a

48. (- 25) × (- 2) =______. Ans: 50 

(-25) × (-2) = x

25 × 2 = x 

49. (- 5) × (- 6) × (- 7) =______. Ans: -210 

(-5) × (-6) × (-7) = x

5 × 6 × (-7) = x

30 × (-7) = x

So, x = -210

50. 3 × (- 1) × (- 15) =_______. Ans: 45 

3 × (-1) × (-15) = x

x = (-3) × (-15) = 45

51. $\left[12 × (- 7)\right]$ × 5 =_____ × (- 7) × ____ Ans: 12, 5 

\[\left[ {12{\text{ }} \times {\text{ }}\left( { - {\text{ }}7} \right)} \right]{\text{ }} \times {\text{ }}5{\text{ }} = {\text{ }}12{\text{ }} \times {\text{ }}\left[ {\left( { - {\text{ }}7} \right){\text{ }} \times {\text{ }}5} \right]\]

52. 23 × (- 99) = ____ × (- 100 + ____) = 23 × ____ + 23 × ____ Ans: 23, 1, -100, 1

23 × (- 99) = 23 × (- 100 + 1) = 23 × (- 100) + 23 × 1

53. ______ × (- 1) = – 35 Ans: 35 

x × (-1) = – 35

54. ____ × (- 1) = 47 Ans: -47 

Let the missing number to be x. 

x × (- 1) = 47

So, x = -47

55. 88 × ____   = – 88 Ans: -1 

88 × x = – 88

56. ____ × (- 93) = 93 Ans: -1 

x × (- 93) = 93

57. (- 40) × ___ = 80 Ans: -2 

(- 40) × x = 80

$ \Rightarrow x = \dfrac{{80}}{{ - 40}} =  - 2$

58. ____ × (-23) = – 920 Ans: 40  

Let a number be multiplied by x. x × (-23) = -920 \[ \Rightarrow x{\text{ }} = {\text{ }} - 920{\text{ }} \div {\text{ }}\left( { - 23} \right){\text{ }} = {\text{ }}\dfrac{{920}}{{23}}{\text{ }} = {\text{ }}40\]

59. When we divide a negative integer by a positive integer, we divide them as whole numbers and put a ____ sign before quotient. Ans: Negative

60. When (-16) is divided by ____ the quotient is 4. Ans: -4 

Let -16 be divided by x gives the quotient 4.

\[ \Rightarrow 4{\text{ }} = \dfrac{{ - 16}}{x} \] \[ \Rightarrow x{\text{ }} = \dfrac{{ - 16}}{4} =  - 4\]

61. Division is the inverse operation of ____. Ans: Multiplication.

62. 65 ÷ (- 13) =_____. Ans: −5

$65 \div \left( { - 13} \right) = x$

$\Rightarrow x = \dfrac{{ - 65}}{{13}} =  - 5$ 

63. (-100) ÷ (-10) =_____. Ans: 10

$\left( { - 100} \right) \div \left( { - 10} \right) = x$

$\Rightarrow x = \dfrac{{100}}{{10}} = 10$ 

64. (-225) ÷ 5 = _____. Ans: −45

$\left( { - 225} \right) \div 5 = x$

$\Rightarrow x = \dfrac{{ - 225}}{5} =  - 45$ 

65. _____ ÷ (-1) = (- 83) Ans: 83 

x ÷ (-1) = – 83

$\Rightarrow x =  - 83 \times \left( { - 1} \right) = 83$ 

66. ____ ÷ (-1) = 75 Ans: −75

$x \div \left( { - 1} \right) = 75$

$\Rightarrow x = 75 \times \left( { - 1} \right) =  - 75$ 

67. 51 ÷ ____ = (-51) Ans: −1

$51 \div x = \left( { - 51} \right)$

$\Rightarrow x = \dfrac{{51}}{{ - 51}} =  - 1$ 

68. 113 ÷ ____ = (- 1) Ans: −113

$113 \div x = \left( { - 1} \right)$

$\Rightarrow x = \dfrac{{113}}{{ - 1}} =  - 113$ 

69. -95 ÷ ____ = 95 Ans: −1

$- 95 \div x = 95$

$\Rightarrow x = \dfrac{{ - 95}}{{95}} =  - 1$ 

70. (-69) ÷ 69 =_____. Ans: −1

$\left( { - 69} \right) \div 69 = x$

$\Rightarrow x = \dfrac{{ - 69}}{{69}} =  - 1$ 

71. (-28) ÷ (-28) = _____ Ans: 1

$\left( { - 28} \right) \div \left( { - 28} \right) = x$

$\Rightarrow x = \dfrac{{ - 28}}{{ - 28}} = 1$ 

Directions: In questions 72 to 108, state whether the statements are true or false. 72. 5 – (-8) is the same as 5 + 8. Ans: True 5 – (-8) = 5 + 8

73. (-9) + (-11) is greater than (-9) – (- 11). Ans: False (-9) + (-11) = – 9 – 11 = -20 And (-9) – (-11) = -9 + 11 = 2 Since, -20 < 2 

⇒ -9 + (-11) < (-9) – (-11)

74. Sum of two negative integers always gives a number smaller than both the integers. Ans: True

75. Difference of two negative integers cannot be a positive integer. Ans: False As -3 – (-5) = -3 + 5 = 2

76. We can write a pair of integers, whose sum is not an integer. Ans: False Since, the sum of two integers is always an integer.

77. Integers are closed under subtraction. Ans: True The subtraction of any two integers is always an integer. So, integers are closed under subtraction.

78. (- 23) + 47 is the same as 47 + (- 23). Ans: True (-23) + 47 = 24 And 47 + (-23) = 47 – 23 = 24

79. When we change the order of integers their sum remains the same. Ans: True

80. When we change the order of integers, their difference remains the same. Ans: False As 2 – 3 – 5 = 2 – 8 = -6 but 3 – 2 – 5 = 3 – 7 = -4

81. Going 500 m towards East first and then 200 m back, is same as going 200 m towards West first and then going 500 m back. Ans: True In the first case, he is at a distance of (500 – 200) m = 300 m towards east. In the second case, he is at a distance of (200 – 500) m = -300 m towards west i.e., 300 m towards east.

82. (-5) × (33) = 5 × (- 33) Ans: True (-5) × (33) = – 165 = 5 × (-33)

83. (-19) × (-11) = 19 × 11 Ans: True (-19) × (-11) = 19 × 11 = 209

84. (-20) × (5 – 3) = (-20) × (-2) Ans: False (-20) × (5 – 3) = (-20) × 2 = (-40) but (-20) × (-2) = 20 × 2 = 40

85. 4 × (-5) = (-10) × (-2) Ans: False 4 × (-5) = – 20 But (-10) × (-2) = 10 × 2 = 20

86. (-1) × (-2) × (-3) = 1 × 2 × 3 Ans: False (-1) × (-2) × (-3) = 1 × 2 × (-3) = 2 × (-3) = (-6) But 1 × 2 × 3 = 6

87. (-3) × 3 = (-12) – (-3) Ans: True Since, (-3) × 3 = (- 9) And (-12) – (-3) = (-12) + 3 = (-9)

88. Product of two negative integers is a negative integer. Ans: False A product of two negative integers is always a positive integer.

89. Product of three negative integers is a negative integer. Ans: True Since, the product of odd numbers of negative integers is always a negative integer.

90. Product of a negative integer and a positive integer is a positive integer. Ans: False A product of a negative integer and a positive integer is a negative integer.

91. When we multiply two integers their product is always greater than both the integers. Ans: False When two integers are multiplied then their product may or may not be greater than both the integers.

92. Integers are closed under multiplication. Ans: True Since, multiplication of two integers is always an integer. Integers are closed under multiplication.

93. (-237) × 0 is the same as 0 × (-39). Ans: True (-237) × 0 = 0 And 0 × (-39) = 0

94. Multiplication is not commutative for integers. Ans: False Multiplication is commutative for integers. For example, 2 x 3 = 6 also 3 x 2 = 6.

95. (-1) is not a multiplicative identity of integers. Ans: True 1 is multiplicative identity for integers.

96. 99 × 101 can be written as (100 – 1) × (100 + 1). Ans: True 99 = 100 – 1 and 101 = 100 + 1 So, 99 × 101 = (100 – 1) × (100 + 1)

97. If a, b and c are integers and b ≠ 0, then a × (b – c) = a × b – a × c Ans: True

Use distributive property of multiplication over subtraction, a × (b – c) = (a × b) – (a × c)

98. (a + b) × c = a × c + a × b Ans: False

Use distributive property of multiplication over addition, a × (b + c) = a × b + a × c

99. a × b = b × a Ans: True

If a = 2 and b = 5, a x b = 2 x 5 = 10

And 5 x 2 = 10

100. a ÷ b = b ÷ a Ans: False As division is not commutative for integers, So, a ÷ b ≠ b ÷ a

101. a – b = b – a Ans: False As subtraction is not commutative for integers. So, a – b ≠ b – a

102. a ÷ (- b) = – (a ÷ b) Ans: True $a \div \left( { - b} \right) = -\dfrac{{  a}}{b}$

$- \left( {a \div b} \right) =  - \dfrac{a}{b}$ 

103. a ÷ (-1) = – a Ans: True \[a \div \left( { - 1} \right) = \dfrac{a}{{ - 1}} =  - a\]

104. Multiplication fact (-8) × (-10) = 80 is the same as division fact 80 ÷ (-8) = (-10). Ans: True (-8) × (-10) = 8 × 10 = 80 And \[80 \div \left( { - 8} \right) = \dfrac{{ - 80}}{8} =  - 10\]

105. Integers are closed under division. Ans: False Consider two integers 3 and 4.

3 ÷ 4 = $\dfrac{3}{4}$ which is not integer. 

So, integers are not closed under division.

106. $\left[ {\left( { - 32} \right) \div 8} \right] \div 2 = - 32 \div \left[ {8 \div 2} \right]$ Ans: False

$\left[ {\left( { - 32} \right) \div 8} \right] \div 2 = \left[ { - \dfrac{{32}}{8}} \right] \div 2 =  - 4 \div 2 = \dfrac{{ - 4}}{2} =  - 2$

But $ - 32 \div \left[ {8 \div 2} \right] =  - 32 \div 4 = \dfrac{{ - 32}}{4} =  - 8$

107. The sum of an integer and its additive inverse is zero (0). Ans: True Let any integer be a. Its additive inverse is -a. a + (-a) = a – a = 0

108. The successor of 0 × (-25) is 1 × (-25). Ans: False 0 × (-25) = 0 and 1 × (-25) = -25 But the successor of 0 is 1.

109. Observe the following patterns and fill in the blanks to make the statements true: (a) – 5 × 4 = – 20 -5 × 3 = -15 = -20 – (-5) -5 × 2 =_____ = -15 – (-5) -5 × 1 =_____ = ______ -5 × 0 = 0 =_______ -5 × -1 = 5 = _____ – 5 × – 2 =__ =______ Ans: -10, -5, -10 – (-5), -5 – (-5), 0 – (-5), 10, 5 – (-5) -5 × 2 = -10 = -15 – (-5) -5 × 1 = -5 = -10 – (-5) -5 × 0 = 0 = -5 – (-5) -5 × -1 = 5 = 0 – (-5) -5 × – 2 =10 = 5 – (-5)

(b) 7 × 4 = 28 7 × 3 =______ = 28 – 7 7 × 2 =______ =____ – 7 7 × 1 = 7  =____ -7 7 × 0 =______ =____ -______ 7 × – 1 = -7 =__ -______ 7 × – 2 =___ =______ -_____ 7 × – 3_____ =____ -______

Ans: 21, 14, 21, 14, 0, 7, 7, 0, 7, -14, -7, 7, -21, -14, 7 7 × 3 = 21 = 28 – 7 7 × 2 = 14 = 21 – 7 7 × 1 = 7  = 14 – 7 7 × 0 = 0 = 7 – 7 7 × (- 1) = -7 = 0 – 7 7 × (- 2) = -14 = -7 – 7 7 × (- 3) = -21 = -14 – 7

110. Science Application An atom consists of charged particles called electrons and protons. Each proton has a charge of +1 and each electron has a charge of -1. Remember number of electrons is equal to number of protons, while answering these questions: (a) What is the charge on an atom? 

Ans: Atoms have two charged particles proton and electron. Protons have +1 charge and electrons have -1 charge. 

Then, total charge = +1 – 1 = 0

(b) What will be the charge on an atom, if it loses an electron?

Ans: If an atom loses an electron, then the charge on the atom will be of proton so charge of atom will be +1.

(c) What will be the charge on an atom, if it gains an electron?

Ans: As calculated in part (a) total charge on atoms is 0. Then the charge on an atom if it gains an electron is -1 i.e. charge of electron gained.

111. An atom changes to a charged particle called an ion, if it loses or gains electrons. The charge on an ion is the charge on electrons plus charge on protons. Now, write the missing information in the table given below:

Ans: Hydroxide ion charge = Proton charge + Electron charge ⇒ -1 = +9 + Electron charge ⇒ Electron charge = -1 – 9 = – 10 Sodium ion charge = Proton charge + Electron charge ⇒ +1 = +11 + Electron charge ⇒ Electron charge = +1 – 11 = -10 Aluminum ion charge = Proton charge + Electron charge ⇒ +13 + (-10) = +13 – 10 = +3 Oxide ion charge = Proton charge + Electron charge ⇒ +8 + (-10) = +8 – 10 = -2

112. Social Studies Application remembering that 1AD came immediately after 1 BC, while solving following problems take 1BC as -1 and 1AD as + 1. (a) The Greco-Roman era, when Greece and Rome ruled Egypt, started in the year 330 BC and ended in the year 395 AD. How long did this era last? Ans: Given 1 BC as -1 and 1 AD as +1. Starting year = 330 BC = (-330) AD Ending year = 395 AD The era lasted for = 395 – (-330) = 395 + 330 = 725 years

(b) Shankaracharya was born in the year 1114 AD and died in the year 1185 AD. What was his age when he died? Ans:  Born year = 1114 AD Death year = 1185 AD So, total age = 1185 – 1114 = 71 years

(c) Turks ruled Egypt in the year 1517 AD and Queen Nefertis ruled. Egypt about 2900 years before the Turks ruled. In what year did she rule? Ans: Turks ruled Egypt in 1517 AD. Queen Nefertis ruled Egypt in (1517-2900) AD= -1383 AD or 1383 BC.

(d) Greek Mathematician Archimedes lived between 287 BC and 212 BC and Aristotle lived between 380 BC and 322 BC. Who lived during an earlier period? Ans: Archimedes lived between 287 BC and 212 BC. Aristotle lived between 380 BC and 322 BC. So, Aristotle lived during an earlier period.

113. The table shows the lowest recorded temperatures for each continent. Write the continents in order from the lowest recorded temperature to the highest recorded temperature.

Ans:   Since, -129° < -90° < -81° < -67° < -27° < -11° < -9° Therefore, the order of the continents from the lowest to the highest recorded temperature is Antarctica, Asia, North America, Europe, South America, Africa, Australia.

114. Write a pair of integers whose product is -12 and there lies seven integers between them (excluding the given integers). Ans: Let the integers be -2 and 6 such that (-2) × 6 = -12 So, a pair of integers is (-2, 6). And there are seven integers, i.e., -1, 0, 1, 2, 3, 4, 5 which lie between -2 and 6.

115. From given integers in Column I, match an integer of Column II, so that their product lies between -19 and -6.

Ans: -5 → 3; 6 → -2; -7 → 1; 8 → -1; -5 × 3 = -15, also -19 < -15 < -6 6 × (-2) = -12, also -19 < -12 < -6 -7 × 1 = -7, also -19 < -7 < -6 8 × (-1) = -8, also -19 < -8 < -6

116. Write a pair of integers, whose product is -36 and whose difference is 15. Ans: Let the integers be 12 and -3 such that 12 × (-3) = -36 and their difference = 12 – (-3) = 12 + 3 = 15 Therefore, a pair of integers is (-3, 12).

117. Match the following:

(b) → (iii)

1 is multiplicative identity.

-a ÷ (-b) = a ÷ b (both signs are cancelled with each other)

(d) → (vii)

a x (-1) = -a

(e) → (viii) 

a x 0 = 0 (any value, when multiplies with 0 becomes zero)

(-a) ÷ b = a ÷ (-b)

0 is an additive identity.

a ÷ (-a) = -a

(i) → (i) 

-a is the additive inverse of a.

118. You have ₹ 500 in your saving account at the beginning of the month. The record below, shows all of your transactions during the month. How much money is in your account after these transactions?

Ans: Money left in the account after given transactions = ₹ (500 + 200 + 150 – 120 – 240) = ₹ (850 – 360) = ₹ 490

119. (a) Write a positive integer and a negative integer whose sum is a negative integer. Ans: 2 + (-3) = -1

(b) Write a positive integer and a negative integer whose sum is a positive integer. Ans: 3 + (-2) = 1

(c) Write a positive integer and a negative integer whose difference is a negative integer. Ans: -1 – (4) = -5

(d) Write a positive integer and a negative integer whose difference is a positive integer. Ans: 4 – (-1) = 5

(e) Write two integers which are smaller than – 5 but their difference is – 5. Ans: -7 < -5, -12 < -5 and -12 – (-7) = -5

(f) Write two integers which are greater than -10 but their sum is smaller than -10. Ans: -5 > -10, -6 >-10 and-5 +(-6) = -11 < -10

(g) Write two integers which are greater than – 4 but their difference is smaller than – 4. Ans: 2 > -4, -3 > -4 and -3 – 2 = -5 < -4

(h) Write two integers which are smaller than – 6 but their difference is greater than – 6. Ans: -7 < -6, -8 < -6 and -7 – (-8) = -7 + 8 = 1 > -6

(i) Write two negative integers whose difference is 7. Ans: -3 – (-10) = -3 + 10 = 7

(j) Write two integers such that one is smaller than -11, and other is greater than -11 but their difference is -11. Ans: -18 < -11; -7 >-11 and -18 – (-7) = -18 + 7 = -11

(k) Write two integers whose product is smaller than both the integers. Ans: (-1) × (2) = -2. Also, -2 < -1 and -2 < 2

(l) Write two integers whose product is greater than both the integers. Ans: 4 × 5 = 20. Also, 4 < 20 and 5 < 20

120. What’s the error? Ramu evaluated the expression – 7 – (-3) and came up with the answer – 10. What did Ramu do wrong? Ans: Ramu did -7 – 3, so he got -10.  

But it should be done like -7 – (-3) = -7 + 3 = -4. Ramu has done addition in place of subtraction.

121. What’s the error? Reeta evaluated -4 + d for d = – 6 and gave an answer of 2. What might Reeta have done wrong? Ans: Since -4 + (-6) = -10, But -4 – (-6) = -4 + 6 = 2 Hence, Reeta has done subtraction in place of addition.

122. The table given below, shows the elevations relative to sea level of four locations. Taking sea level as zero (0), answer the following questions.

(a) Which location is closest to sea level?

Ans: C is closest to sea level.

(b) Which location is farthest from sea level? Ans: D is farthest from sea level.

(c) Arrange the locations from the least to the greatest elevation. Ans: Since, -180 < -55 < 1600 < 3200. Therefore, the location from the least to the greatest elevation is A < C < B < D.  

123. You are at an elevation 380 m above sea level as you start a motor ride. During the ride, your elevation changes by the following meters 540 m, -268 m, 116 m, -152 m, 490 m, -844 m, 94 m. What is your elevation relative to the sea level at the end of the ride? Ans: Elevation relative to the sea level at the end of the ride = [380 + 540 – 268 + 116 -152 + 490 – 844 + 94]m = [380 + 540 + 116 + 490 + 94 – 268 – 152 – 844] m = [1620 – 1264] m = 356 m

124. Evaluate the following, using distributive property. (i) -39 × 99

Ans: -3861 

$- 39{\text{ }} \times {\text{ }}99{\text{ }} = {\text{ }} - 39{\text{ }} \times {\text{ }}\left( {100{\text{ }} - 1} \right)$ 

 $={\text{ }} - 39{\text{ }} \times {\text{ }}100{\text{ }} + {\text{ }}\left( { - 39} \right){\text{ }} \times {\text{ }}\left( { - 1} \right)$ 

 $={\text{ }} - 3900{\text{ }} + {\text{ }}39{\text{ }}$ 

 $={\text{ }} - 3861$ 

(ii) (-85) × 43 +43 × (-15) Ans: $\left( { - 85} \right){\text{ }} \times {\text{ }}43{\text{ }} + {\text{ }}43{\text{ }} \times {\text{ }}\left( { - 15} \right) = {\text{ }}43{\text{ }} \times {\text{ }}\left( { - 85} \right){\text{ }} + {\text{ }}43{\text{ }} \times {\text{ }}\left( { - 15} \right)$ 

 $={\text{ }}43{\text{ }} \times {\text{ }}\left[ { - 85{\text{ }}-{\text{ }}15} \right]$ 

 $={\text{ }}43{\text{ }} \times {\text{ }}\left[ { - 100} \right]{\text{ }}$ 

 $={\text{ }} - 4300$ 

(iii) 53 × (-9) – (-109) × 53 Ans:   $53{\text{ }} \times {\text{ }}\left( { - 9} \right){\text{ }}-{\text{ }}\left( { - 109} \right){\text{ }} \times {\text{ }}53 = {\text{ }}53{\text{ }} \times {\text{ }}\left( { - 9} \right){\text{ }}-{\text{ }}53{\text{ }} \times {\text{ }}\left( { - 109} \right)$ 

 $={\text{ }}53{\text{ }} \times {\text{ }}\left[ {\left( { - 9} \right){\text{ }}-{\text{ }}\left( { - 109} \right)} \right]$ 

 $={\text{ }}53{\text{ }} \times {\text{ }}\left[ { - 9{\text{ }} + {\text{ }}109} \right]{\text{ }}$ 

 $={\text{ }}53{\text{ }} \times {\text{ }}100{\text{ }}$ 

 $={\text{ }}5300$ 

(iv) 68 × (-17) + (-68) × 3 Ans: $68{\text{ }} \times {\text{ }}\left( { - 17} \right){\text{ }} + {\text{ }}\left( { - 68} \right){\text{ }} \times {\text{ }}3{\text{ }} = {\text{ }}68{\text{ }} \times {\text{ }}\left( { - 17} \right){\text{ }} + {\text{ }}68{\text{ }} \times {\text{ }}\left( { - 3} \right)$ 

 $={\text{ }}68{\text{ }} \times {\text{ }}\left[ {\left( { - 17} \right){\text{ }} + {\text{ }}\left( { - 3} \right)} \right]$ 

 $={\text{ }}68{\text{ }} \times {\text{ }}\left( { - 20} \right){\text{ }}$ 

 $={\text{ }} - 1360$ 

125. If ‘*’ is an operation for integers a and b. We have a * b = a × b + (a × a + b × b), then find (i) (-3) * (-5) Ans: We have, 

a * b = a × b +(a × a + b × b) Now, put a = (-3) and b = (-5) (-3)* (-5) = (- 3) × (- 5)+ $\left[(- 3) × (- 3)+ (- 5) × (- 5)\right]$ = 15 + (9 + 25) = 15 + 34 = 49

(ii) (-6) * 2 Ans: Put a = – 6 and b = 2 (-6) * 2 = (-6) × 2 + $\left[(-6) × (-6) + 2 × 2\right]$ = -6 × 2 + (36 + 4) = -12 + 40 = 28

126. If Δ is an operation such that for integers a and b we have a Δ b = a × b – 2 × a × b + b × b (-a) × b + b × b then find (i) 4 Δ (- 3) (ii) (- 7) Δ (- 1) Also show that 4 Δ (- 3) ≠ (- 3) Δ 4  and (-7) Δ (-1) ≠ (-1) Δ (- 7) Ans:  Given, a Δ b = a × b – 2 × a × b + b × b (-a) × b + b × b (i) 4 Δ (-3) = 4 × (-3) – 2 × 4 × (-3) + (-3) × (-3)(-4) × (-3) + (-3) × (-3) 

= -12 + 24 + 108 + 9 = -12 + 141 = 129

(ii) (-7) Δ (-1) = (-7) × (-1) – 2 × (-7) × (-1) + (-1) × (-1) (7) × (-1) + (-1) × (-1) 

= 7 – 14 – 7 + 1 = 8 – 21 = -13

Now, (-3) Δ 4 = (-3) × 4 – 2 × (-3) × (4) + 4 × 4(3) × 4 + 4 × 4 = -12 + 24 + 192 + 16 = -12 + 232 = 220 But 4 Δ (-3) = 129 Therefore, 4 Δ (-3) ≠ (-3) Δ 4. And, (-1) Δ (-7) = (-1) × (-7) – 2 × (-1) × (-7) + (-7) × (-7)(1) × (-7) + (-7) × (-7) = 7 – 14 – 343 + 49 = 56 – 357 = -301 But (-7) Δ (-1) = -13 Therefore, (-7) Δ (-1) ≠ (-1) Δ (-7).

127. Below u, v, w and x represent different integers, where u = (-4) and x ≠ 1. By using following equations, find each of the values u × v = u x × w =w u + x = w Explain your reason, using the properties of integers

Ans: As u × v = u and u = -4 

∴ -4 × v = -4 ⇒ v = l (Multiplicative identity)

Ans: As x × w = w. Given that x ≠ 1 ∴ x × w = w is only possible when w = 0

Ans: As u + x = w, 

Put u = – 4 and w = 0 ∴ -4 + x = 0 ⇒ x = 4 (Transposing -4 to R.H.S.)

128. Height of a place A is 1800 m above sea level. Another place B is 700 m below sea level. What is the difference between the levels of these two places? Ans: Difference between the levels of places A and B is $\left[1800 – (-700)right]$ m = (1800 + 700)m = 2500 m

129. The given table shows the freezing points in °F of different gases at sea level. Convert each of these into °C to the nearest integral value using the relation and complete the table,

\[C{\text{ }} = {\text{ }}\dfrac{5}{9}\left( {F - 32} \right)\]

Given relation is \[C{\text{ }} = {\text{ }}\dfrac{5}{9}\left( {F - 32} \right)\]. 

For hydrogen,

$C{\text{ }} = {\text{ }}\dfrac{5}{9}\left( { - 435 - 32} \right) = \dfrac{5}{9}\left( { - 467} \right)$

 $=\dfrac{{ - 2335}}{9} =  - 259.44{\text{ }}^\circ {\text{C}}$ 

So, the nearest integer value is -259°C.

For Krypton,

$C{\text{ }} = {\text{ }}\dfrac{5}{9}\left( { - 251 - 32} \right) = \dfrac{5}{9}\left( { - 283} \right)$

 $=\dfrac{{ - 1415}}{9} =  - 157.22{\text{ }}^\circ {\text{C}}$ 

So, the nearest integer value is -157°C.

For Oxygen,

$C{\text{ }} = {\text{ }}\dfrac{5}{9}\left( { - 369 - 32} \right) = \dfrac{5}{9}\left( { - 401} \right)$

 $=\dfrac{{ - 2005}}{9} =  - 222.77{\text{ }}^\circ {\text{C}}$ 

So, the nearest integer value is -222°C.

For Helium,

$C{\text{ }} = {\text{ }}\dfrac{5}{9}\left( { - 458 - 32} \right) = \dfrac{5}{9}\left( { - 490} \right)$

 $=\dfrac{{ - 2450}}{9} =  - 272.22{\text{ }}^\circ {\text{C}}$ 

So, the nearest integer value is -272°C.

$C{\text{ }} = {\text{ }}\dfrac{5}{9}\left( { - 309 - 32} \right) = \dfrac{5}{9}\left( { - 341} \right)$

 $=\dfrac{{ - 1705}}{9} =  - 189.44{\text{ }}^\circ {\text{C}}$ 

So, the nearest integer value is -189°C.

130. Sana and Fatima participated in an apple race. The race was conducted in 6 parts. In the first part, Sana won by 10 seconds. In the second part, she lost by 1 min, then won by 20 seconds in the third part and lost by 25 seconds in the fourth part, she lost by 37 seconds in the fifth part and won by 12 seconds in the last part. Who won the race finally? Ans: Taking winning by time be a positive integer and losing by time be a negative integer. Therefore, Sana’s total time (winning or losing the race) = (10 – 60 + 20 – 25 – 37 + 12) seconds = (42 – 122) seconds = -80 seconds Hence, Sana lost the race by 80 seconds or 1 minute 20 seconds i.e., Fatima won the race finally.

131. A green grocer had a profit of ₹ 47 on Monday, a loss of ₹ 12 on Tuesday and loss of ₹ 8 on Wednesday. Find his net profit or loss in 3 days. Ans: Taking profit as a positive integer and loss as negative integer, we have grocer’s net profit or loss in 3 days = ₹ (47 – 12 – 8) = ₹ 27 Therefore, the grocer has a profit of ₹ 27.

132. In a test, +3 marks are given for every correct answer and -1 mark are given for every incorrect answer. Sona attempted all the s and scored +20 marks, though she got 10 correct answers. (i) How many incorrect answers has she attempted?

Ans: Total marks scored by Sona = 20 Total correct answers = 10 ∴ Marks for correct answers = 10 × 3 = 30 but she got 20 marks. ∴ Marks for incorrect answers = 20 – 30 = – 10 -1 mark is given for every incorrect answer. Therefore, total incorrect answers = $\dfrac{{ - 10}}{{ - 1}} = 10$

(ii) How many questions were given in the test? Ans: Total correct answers = 10 Total incorrect answers = 10 (From (i) part) Therefore, total questions given in the test = 10 + 10 = 20

133. In a true-false test containing 50 s, a student is to be awarded 2 marks for every correct answer and -2 for every incorrect answer and 0 for not supplying any answer. If Yash scored 94 marks in a test, what are the possibilities of his marking correct or wrong answer? Ans: Yash secured = 94 marks So, minimum correct answers = 94 ÷ 2 = 47 Now, there can be two possibilities : (1) He attempted 47 correct answers and 3 un-attempted. (2) He attempted 48 correct and 1 un-attempted and 1 wrong answer.

134. A multistory building has 25 floors above the ground level each of height 5 m. It also has 3 floors in the basement, each of height 5m. A lift in a building moves at a rate of 1 m/s. If a man starts from 50m above the ground, how long will it take him to reach the 2nd floor of the basement? Ans: Height of each floor = 5 m ∴ Height below the basement to be covered = 2 × 5m = 10m If a man starts from 50 m above ground level and reach the 2nd floor of the basement. ∴ His total distance to be covered = (50 + 10) m = 60 m Rate of moving of a lift = 1 m/s ∴ A man reach at 2nd floor of basement in 1 × 60 = 60 seconds or 1 minute.

135. Taking today as zero on the number line, if the day before yesterday is 17 January, what is the date 3 days after tomorrow? Ans:  

The day before yesterday was 17 January. So, today is 19 January. The date 3 days after tomorrow will be 20 January + 3 days = 23 January

136. The highest point measured above sea level is the summit of Mt. Everest, which is 8,848 m above sea level and the lowest point is challenger deep at the bottom of Mariana Trench which is 10,911 m below sea level. What is the vertical distance between these two points? Ans: The highest point (above sea level) = 8,848 m The lowest point (below sea level) = 10,911 m Therefore, total vertical distance between two points = [8,848 – (-10,911)] m = [8,848 + 10,911] m = 19,759 m

The NCERT Exemplar for Class 7 Math Solutions Chapter 1 Integers is available on Vedantu in PDF format for free download. This PDF contains all the NCERT Exemplar Class 7 Math Chapter 1 Integers questions and their answers to assist students in their revisions and exam preparations. Since Integers is one of the most important concepts of math, the  NCERT Exemplar for Class 7 Math Solutions Chapter 1 Integer PDF will surely give you an advantage in the exam. It will help you get better at solving Integer questions and enable you to score the highest marks in your class. Most of the questions in your final exams are quite similar to the ones in the  NCERT Exemplar for Class 7 Math Solutions Chapter 1 Integers PDF. That is why you should go through the entire PDF before you appear for your Class 7 Math exam.

What Do You Learn in the Class 7 Math Chapter 1- Integers? 

Here is the syllabus of what you will learn in the Class 7 Math Chapter 1 Integers: 

Introduction to Integers

Natural Numbers

Whole Numbers

Properties of Addition and Subtraction of Integers

Closure under Addition and subtraction

Commutativity Property for addition

Associativity Property for addition

Additive Identity & Additive Inverse

Additive Identity

Additive inverse

Properties of Multiplication of Integers

Closure under Multiplication

Commutative Property of Multiplication

Multiplication by Zero

Multiplicative Identity

Associative property of Multiplication

Distributive Property of Integers

Division of Integers

Dividing a negative integer by a positive integer

Dividing a positive integer by a negative integer

Dividing a negative integer by a negative integer

The Number Line

Representing integers on a number line 

Addition and subtraction of integers using a number line

Addition and Subtraction of Integers

The absolute value of integers

Addition of two positive integers

Addition of two negative integers

Addition of a positive and negative integer

Introduction to Zero

Addition of zero to an integer 

Subtraction of zero from an integer, or vice versa

Multiplying an integer with zero 

Division of zero by an integer 

Properties of Division of Integers

Commutativity

Closure  

Multiplication of Integers

Product of two positive integers 

Product of two negative integers

Product of one positive and one negative integer 

FAQs on NCERT Exemplar for Class 7 Maths Solutions Chapter 1 Integers

1. How to download the NCERT Exemplar for Class 7 Maths Solutions Chapter 1 Integers?

Downloading the NCERT Exemplar for Class 7 Maths Solutions Chapter 1 Integers is not that difficult. All you have to do is visit Vedantu’s website, sign up, look for the NCERT Exemplar for Class 7 Maths Solutions Chapter 1 Integers, and download its PDF file. Apart from this PDF, you will find an unlimited stock of study materials on our website. You can download all these files without spending a single penny. Vedantu does not charge any registration fee and provides all the study resources for free.

2. Is the NCERT Exemplar for Class 7 Maths Solutions Chapter 1 Integers useful?

Yes, the  NCERT Exemplar for Class 7 Maths Solutions Chapter 1 Integers is quite helpful for the students. It contains solutions to the NCERT exemplar questions that will help them in their exam preparations. It will help you revise Chapter 1 Integers, which is an important part of the syllabus. An integer is a concept that will come in handy in the subsequent classes. That is why you should go through the  NCERT Exemplar for Class 7 Maths Solutions Chapter 1 Integer to understand every aspect of the chapter.   

3. Is the NCERT Exemplar for Class 7 Maths Solutions Chapter 1 Integer enough to prepare for the exams?

Yes, the  NCERT Exemplar for Class 7 Maths Solutions Chapter 1 Integers will be enough for you to revise the chapter and prepare for your exam. It contains many questions that you will not find in any other textbook or reference book. There is a high probability of these types of questions appearing in your exams. So, you won’t need any sample papers or previous year question papers to look for questions related to the Class 7 Maths Chapter 1 Integers.

4. Why is it necessary to download the NCERT Exemplar for Class 7 Maths Solutions Chapter 1 Integers PDF?

It is necessary to download the NCERT Exemplar for Class 7 Maths Solutions Chapter 1 Integer PDF as it contains more than a hundred questions. There is a high probability of these types of questions coming in your exams. Since all the concepts of maths require written practice, solving these questions can be helpful for exam preparations. If you get stuck on any of these questions, you can look at the answers to know how to solve them.

5. Does the NCERT Exemplar for Class 7 Maths Solutions Chapter 1 Integers provide answers in detail?  

Yes, the NCERT Exemplar for Class 7 Maths Solutions Chapter 1 Integers provides you with detailed answers to all the questions. Even for MCQs, there is an explanation as to why a particular option is right. For very short, short, and long answer type questions, you will find step-by-step solutions to help you understand the answers. It will also show you how you can solve Class 7 Maths Chapter 1 Integers questions in the correct sequence of steps and gain full marks. 

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Case Study Questions for Class 10 Maths Chapter 1 Real Numbers

• Last modified on: 1 year ago
• Reading Time: 7 Minutes

Question 1:

HCF and LCM are widely used in number system especially in real numbers in finding relationship between different numbers and their general forms. Also, product of two positive integers is equal to the product of their HCF and LCM Based on the above information answer the following questions.

(i) If two positive integers x and y are expressible in terms of primes as x =p 2 q 3 and y=p 3 q, then which of the following is true? (a) HCF = pq 2 x LCM (b) LCM = pq 2 x HCF (c) LCM = p 2 q x HCF (d) HCF = p 2 q x LCM

(ii) A boy with collection of marbles realizes that if he makes a group of 5 or 6 marbles, there are always two marbles left, then which of the following is correct if the number of marbles is p? (a) p is odd (b) p is even (c) p is not prime (d) both (b) and (c)

(iii) Find the largest possible positive integer that will divide 398, 436 and 542 leaving remainder 7, 11, 15 respectively. (a) 3 (b) 1 (c) 34 (d) 17

(iv) Find the least positive integer which on adding 1 is exactly divisible by 126 and 600. (a) 12600 (b) 12599 (C) 12601 (d) 12500

(v) If A, B and C are three rational numbers such that 85C – 340A = 109, 425A + 85B = 146, then the sum of A, B and C is divisible by (a) 3 (b) 6 (c) 7 (d) 9

Question 2:

To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.

(i) What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B? (a) 144 (b) 128 (c) 288 (d) 272

(ii) If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32 , 36) is (a) 2 (b) 4 (c) 6 (d) 8

(iii) 36 can be expressed as a product of its primes as (a) (b) (c) (d)

(iv) 7 is a (a) Prime number (b) Composite number (c) Neither prime nor composite (d) None of the above

(v) If p and q are positive integers such that p = a and q= b, where a , b are prime numbers, then the LCM (p, q) is (a) ab (b) a 2 b 2 (c) a 3 b 2 (d) a 3 b 3

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Chapter 1 Real Numbers Chapter 2 Polynomials Chapter 3 Pair of Linear Equations in Two Variables C hapter 4 Quadratic Equations Chapter 5 Arithmetic Progressions Chapter 6 Triangles Chapter 7 Coordinate Geometry Chapter 8 Introduction to Trigonometry Chapter 9 Some Applications of Trigonometry Chapter 10 Circles Chapter 11 Constructions Chapter 12 Areas Related to Circles Chapter 13 Surface Areas and Volumes Chapter 14 Statistics Chapter 15 Probability

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Home » 7th Class » Class 7 Maths Notes for Integers (PDF) – Study Material

Class 7 Maths Notes for Integers (PDF) – Study Material

Class 7 Maths Integers – Get here the Notes, Question & Practice Paper of Class 7 Maths for topic Integers Notes. Integers Notes for Class 7 Maths are here. You can download the Integers Notes PDF to study all the topics in this chapter. Moreover the Class 7 Maths notes include chapter summary, definitions, examples, and key pointers for Integers . Thus if you are studying class Maths (गणित), then the  Integers notes  will help you easily understand the topic and ace it.

Class 7 Maths Notes for Integers

Integers is a critical part in the study of Maths . In India, it is taught in class. Therefore the Class 7 Notes for Maths topic Integers have been compiled by teachers and field experts. They explain the complete chapter of Integers in one-shot .

Integers Notes Download Link – Click Here to Download PDF

Integers Notes for Class 7 Maths

Integers Class 7 notes is as follows. You can view the document here and also download it use it anytime for future reference whenever you want to brush up your concepts of Maths.

Chapter 1 – Integers

Previous Knowledge:

Integers – Integers are bigger collection of numbers which is formed by whole numbers and their negatives or we can say that all positive and negative numbers including zero are integers. Example: -3, -2, -1, 0, 1, 2, 3…

Integers on Number Line – On a number line, when we:

• add a positive integer, we move to the right.
• add a negative integer, we move to the left.
• subtract a positive integer, we move to the left.
• subtract a negative integer, we move to the right.

Properties of Addition and Subtraction of Integers

(a) Closure Property: Integers are closed for addition and subtraction both, i.e. a + b and a – b are again integers, where a and b are any integers. Example: For any two integers 2 and 3, we have 2+ 3 = 5 an integer and 2 – 3 = -1 is also an integer.

(b) Commutative Property: Addition is commutative for integers, i.e. a + b = b + a for all integers a and b. Example: For any two integers say 5 and 4, we have 5+ 4 = 4 + 5 = 9, but the same does not holds for subtraction as 5– 4 =1 and 4 – 5 = -1.

(c) Associative Property: Addition is associative for integers, i.e., (a + b) + c = a + (b + c) for all integers a, b and c. Example: For any three integers say 6, 3 & 7 we have (6 + 3) +7= 6 + (3 + 7) Again it does not hold under subtraction.

(d) Additive Identity: Integer 0 is the identity under addition i.e. a + 0 = 0 + a = a for every integer a. Example: 3 + 0 = 0 + 3 = 3

Multiplication of Integers

The product of a positive and a negative integer is a negative integer, whereas the product of two negative integers is a positive integer and the product of two positive integers is always a positive integer. Example: – 2 × 7 = – 14 and – 3 × – 8 = 24 and 5 × 6 = 30.

Also we can see that the product of even number of negative integers is positive. whereas the product of odd number of negative integers is negative.

Example: (-1) × (-1) × (-1) × (-1) = 1 but (-1) × (-1) × (-1) = -1.

Properties of Multiplication of Integers

(a) Closure Property: Integers are closed under multiplication, i.e., a × b is an integer for any two integers a and b, Example: 2 x 3 =6, 6 is also an integer.

(b) Commutative Property: Multiplication is commutative for integers, i.e., a × b = b × a for any integers a and b Example: 4 x 3 = 3 x 4 = 12.

(c) Associative Property: Multiplication is associative for integers, i.e., (a × b) × c = a × (b × c) for any three integers a, b & c. Example: (2 × 3) × 4 = 2 × (3 × 4) = 24

(d) Multiplicative Identity: The integer 1 is the identity under multiplication, i.e., 1 × a = a × 1 = a for any integer a. Example: 1 × 9 = 9 × 1 = 9

(e) Distributive Property: Under addition and multiplication, integers show a property called distributive property i.e., a × (b + c) = (a × b) + (a × c) for any three integers a, b and c. Examples: i) 16 x12 = 16 x (10 +2) = (16 x 10) + (16 x 2) = 160 + 32 =192 ii) -23 x 48 = -23 x (50 – 2) = (-23 x 50) + (-23 x 2) = -1150 + (-46) = -1150 – 46 = -1196 iii) 52 x (-8) + (-52) x 2 = [52 x (-8)] + [ 52 x (-2)] = 52 x [(-8 -2)] =52 x (-10) = -520.

Properties of Division of Integers

(a) When a positive integer is divided by a negative integer, the quotient obtained is a negative integer and vice-versa. Example: 2/−3 = – 2/3 (b) Division of a negative integer by another negative integer gives a positive integer as quotient. Example: −5 / −6 = 5 / 6

Other Properties of Integer: For any integer a, we have (i) a ÷ 0 is not defined and (ii) a ÷ 1 = a. Example: 4÷0 is not defined and 6 ÷1 = 6

Candidates who are ambitious to qualify the Class 7 with good score can check this article for Notes, Study Material, Practice Paper. Above we provided the link to access the Notes , Important Question and Practice Paper of Class 7 Maths for topic Integers.

All Topics Class 7 Maths Notes

Chapter wise notes for Maths (गणित) are given below.

• Fractions and Decimals
• Data Handling
• Simple Equations
• Lines & Angles
• Triangles & Its Properties
• Comparing Quantities
• Rational Numbers
• Perimeter and Area
• Algebraic Expressions
• Exponents and Powers
• Visualing Solid Shapes

Class 7 Notes for All Subjects

• Class 7 Maths Notes
• Class 7 Science Notes

NCERT Solutions for Class 7 Maths Integers

The Integers notes here help you solve the questions and answers . Also, you can complete the Class 7 Integers worksheet using the same. In addition you will also tackle CBSE Class 7 Maths Important Questions with these Class 7 notes .

However if you still need help, then you can use the NCERT Solutions for Class 7 Maths Integers to get all the answers. Integers solutions contain questions, answers, and steps to solve all questions.

Notes for All Classes

• Class 6 Notes
• Class 7 Notes
• Class 8 Notes
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• Class 10 Notes
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Integers Notes for Class 7 Maths – An Overview

Class 7 Integers Notes for All Boards

You can use the Class 7 Maths notes of Integers for all boards.

The education boards in India for which Integers notes are relevant are – CBSE, CISCE, AHSEC, CHSE Odisha, CGBSE, HBSE, HPBOSE, PUE Karnataka, MSBSHSE, PSEB, RBSE, TBSE, UPMSP, UBSE, BIEAP, BSEB, GBSHSE, GSEB, JAC, JKBOSE, KBPE, MBOSE, MBSE, MPBSE, NBSE, DGE TN, TSBIE, COHSEM, WBCHSE .

Therefore you can refer to these notes as CBSE, CISCE, AHSEC, CHSE Odisha, CGBSE, HBSE, HPBOSE, PUE Karnataka, MSBSHSE, PSEB, RBSE, TBSE, UPMSP, UBSE, BIEAP, BSEB, GBSHSE, GSEB, JAC, JKBOSE, KBPE, MBOSE, MBSE, MPBSE, NBSE, DGE TN, TSBIE, COHSEM, WBCHSE notes for class Class 7 / Class / Maths for the topic Integers.

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• Internet Services and Mobile Technologies Class 10 Case Study Computer Applications Chapter 2

Last Updated on September 16, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 10 computer applications. Case study questions or passage based questions are the new question format that is introduced in CBSE board. The resources for case study questions or passage based questions are very less. So, to help students we have created chapterwise case study and passage based questions for class 10 computer applications. In this article, you will find case study for CBSE Class 10 Computer Applications Chapter 2 Internet Services and Mobile Technologies. It is a part of Case Study Questions for CBSE Class 10 Computer Applications Series.

Table of Contents

Case Study Questions on Internet Services and Mobile Technologies Class 10

Read the given passage carefully and answer the following questions:

Internet Browsing: Coursera has partnered with museums, universities, and other institutions to offer students free classes on an astounding variety of topics. Students can browse the list of available topics or simply answer the question “What would you like to learn about?”, then when they answer that question they are led to a list of available courses on that topic. Students who are nervous about getting in over their heads can relax.

Q. 1. “A combination of both face-to-face, traditional classroom methods with e-learning to create a hybrid approach to teaching”. What is this type of e-learning?

Q. 2. What type involves allowing participants to complete training in their own time via webbased training i.e., e-mail, blackboard, intranets, and where there is no help from instructors and participants can use Internet as a support tool?

Q. 3. Give some examples of an e-learning website.

Q. 4. Give two benefits of virtual classroom.

• It is a type of blended learning.
• Asynchronous learning.
• edX, MasterClass and SimplyCoding are some example of an e-learning website.
• Benefits of virtual classroom are: (i) Teachers interact with students in real line. (ii) Students can voice their questions and interact with peers.

Basic HTML Elements Class 10 Case Study Computer Applications Chapter 3

Introducing internet class 10 case study computer applications chapter 1, frequently asked questions (faqs) on internet services and mobile technologies class 10 case study, q1: what are case study questions.

A1: Case study questions are a type of question that presents a detailed scenario or a real-life situation related to a specific topic. Students are required to analyze the situation, apply their knowledge, and provide answers or solutions based on the information given in the case study. These questions help students develop critical thinking and problem-solving skills.

Q2: How should I approach case study questions in exams?

A2: To approach case study questions effectively, follow these steps: Read the case study carefully: Understand the scenario and identify the key points. Analyze the information: Look for clues and relevant details that will help you answer the questions. Apply your knowledge: Use what you have learned in your course to interpret the case study and answer the questions. Structure your answers: Write clear and concise responses, making sure to address all parts of the question.

Q3: What are the benefits of practicing case study questions from your website?

A3: Practicing case study questions from our website offers several benefits: Enhanced understanding: Our case studies are designed to deepen your understanding of historical events and concepts. Exam preparation: Regular practice helps you become familiar with the format and types of questions you might encounter in exams. Critical thinking: Analyzing case studies improves your ability to think critically and make connections between different historical events and ideas. Confidence: Practicing with our materials can boost your confidence and improve your performance in exams.

Q10: How many type of chat services are available online? Name them.

A4: There are three most common types of chat services available online which are: (i) Instant Messaging. (ii) ICQ (I Seek You). (iii) IRC (Internet Relay Chat).

Q5: How multiple e-mail addresses are defined in to, Cc, Bcc field?

A5: By using comma between e-mail addresses.

Q6: What do you understand by remote login?

A6: Remote login or remote access is the ability to get access to a computer or a network from a different computer.

Q7: Distinguish between FTP and Telnet

A7: FTP (File Transfer Protocol) facilitates the transfer of files from one point to another while Telnet is a connection protocol that allows a user to connect to a remote server.

Q8: What is the significance of URL?

A8: The URL (Uniform Resource Locator) specifies the address of a file and every file on the Internet has a unique address

Q9: When using a search engine, what does a minus sign used with keywords in the search box mean?

A9: Search engine is a website that provides the required data on specific content. It also allows users to enter keywords related to particular topics and retrieve information. The minus sign in front of a word or phrase means that it includes first term but not the second term.

Q10: What do you understand by e-reservation?

A10: E-reservation or online reservation is the process of booking tickets such as for movies, airlines, buses and trains using the Internet.

Q11: How does FTP work?

A11: FTP works on the principle of a client/server model. A FTP client program enables the user to interact with a FTP server program in order to access information and services on the server computer. To access FTP server program, users must be able to connect to the Internet or interact with FTP client program.

Q12: Are there any online resources or tools available for practicing “ Internet Services and Mobile Technologies” case study questions?

A12: We provide case study questions for CBSE Class 10 Computer Applications on our  website . Students can visit the website and practice sufficient case study questions and prepare for their exams.

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