integers problem solving with answers

Math Problems and Solutions on Integers

Problems related to integer numbers in mathematics are presented along with their solutions.

Challenge Exercises Integer Word Problems

Directions:  Read each question below. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.  Each answer should be given as a positive or a negative integer.  Do not enter commas in your answers.

Hints:  Always double check the sign of your answer. Does it make sense for the problem? When subtracting integers, be sure to subtract the smaller integer from the larger integer. The smaller integer is farther to the left on the number line.

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Last modified on August 3rd, 2023

Integer Word Problems

We use integers in our everyday life for counting money and measuring the speed of sound and light, height and weight of objects, temperature and pressure of the atmosphere, and depth of a sea. Solving word problems related to the above measurements will help us relate better to the concept with applications.

A submarine was located 600 feet below sea level. Calculate its new position if it ascends 250 feet from its position.

Given, The initial position of the submarine is 600 feet It ascends 250 feet Thus, the new position of the submarine is (600 – 250) feet = 350 feet Thus, the new depth of the submarine is 550 feet

Today’s weather report suggested that the temperature of New York City increased from 10-degree celsius to 20-degree celsius. What is the rise in temperature?

Given, Initial temperature = -10 degree celsius Final temperature = 20 degrees celsius Increase in temperature = 20 – (-10) = 30 degrees celsius Thus, the rise in temperature of New York City is 30 degree Celsius.

Demitri owes her mother \$5.00. He earns \$12.00 doing chores. How much is left with him after he gives his mother what she owes?

Given, Amount to be given to his mother = \$5.00 He earns = \$12.00 Thus, he is left with = \$(12.00 – 5.00) = \$7.00 Thus, Demitri is left with \$7.00.

The local movie theater reported losses of \$475 each day for 3 days. What was the total loss incurred for the 3 days?

Given, Loss incurred by the movie theater per day = \$475 The loss incurred in 3 days = \$(3 × 475) = \$1,425 Thus the total loss incurred by the movie theater in 3 days is \$1,425

The Second World War began in the year 1939 and ended in 1945. How long did it last?

Given, The Second World War began in 1939 and ended in 1945 Thus, it lasted (1945 – 1939) = 6 years

Mt. Everest is 29,028 feet above sea level, and the Dead Sea is 1,312 feet below sea level. Find the difference between the 2 elevations.

Given The height of Mt. Everest is 29,028 feet above sea level The height of the Dead Sea is 1,312 feet below sea level Thus, the difference between the 2 elevations = (29,028 + 1,312) feet = 30,340 feet

Dakota withdrew a total of \$600 over 4 days. If he withdrew the same amount daily, find the amount he withdrew each day.

Given, Total amount Dakota withdrew = \$600 Number of days he withdrew = 4 days Amount withdrawn each day = \$(600 ÷ 4) = \$150 Thus, Dakota withdrew \$150 per day.

Andrew had \$12,000 in his account. He once withdrew \$2,000 and then deposited $6,000. What is the current balance in the account?

Given, Initial balance Andrew had = \$12,000 Amount withdrawn = \$2,000 Amount deposited = \$6,000 Thus, the current balance = \$(12,000 – 2,000 + 6,000) = \$16,000 Thus, the current balance Andrew has currently in his account is \$16,000

A kite rises 100 feet from the ground and then falls back 40 feet. What is the current height of the kite from the ground?

Given, The kite rises = 100 feet and then falls back = 40 feet Thus, the current height of the kite from the ground is (100 – 40) feet = 60 feet

If it is 3°C outside and the temperature drops 15° C in the next 6 hours, how cold will it be after 6 hours?

Initially, the outside temperature was 2°C Then, the temperature drops to = (2 – 15)°C  = -13°C Thus, the temperature after 6 hours will be -13°C

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Integer Word Problems

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Integer Word Problems

Welcome to the fascinating world of integer word problems! Don’t let the fancy name scare you off; these problems might be easier and more fun than you think. Simplifying them is handy in daily life, and they’ll reappear in various forms throughout your academic journey. Let’s dive into the fundamental components.

What are Integer Word Problems?

In essence, integer word problems are mathematical problems involving number-related questions in the form of a story or practical situation. Specifically, these problems use integers — whole numbers that can be positive, negative, or zero. For instance, you might be asked how many more books Mike read than Sarah if Mike reads 15 and Sarah reads 7. Since you’re subtracting 7 from 15, you’re dealing with an integer word problem.

Importance of Solving Integer Word Problems

Mastering integer word problems plays a significant role in building your mathematical expertise. They help improve your problem-solving skills and enhance your ability to think logically and critically. Moreover, these problems are a cornerstone of real-world situations. Whether you are calculating the distance between two cities, determining profit and loss in business, or even figuring out temperature changes, integers and their problems come into play.

How to Solve Integer Word Problems

Are you ready to tackle integer word problems? Here are a few steps:

• Understand the Problem:  Breaking the problem into smaller parts makes it less daunting. Take your time to understand what the problem is about.
• Identify the Key Information:  Highlight or underline important facts or figures in the problem. Look for clues indicating whether you’re dealing with addition, subtraction, or a combination.
• Formulate a Plan:  Write down your actions to arrive at the solution.
• Execute Your Plan:  Apply the actions you’ve mapped out to solve the problem.
• Verify Your Answer:  Always double-check your outcome. Does it make sense in terms of the problem?

In dealing with integer word problems, practice is critical. The more problems you tackle, the more proficient you become. Happy problem-solving!

Basic Concepts of Integers

As a student or math enthusiast, knowing and mastering the basic concepts of integers will help you understand and tackle integer word problems better. In this section, we’ll delve into the definitions of integers, further distinguishing between positive and negative integers.

Defining Integers

Integers  are a number category that includes all the whole numbers, their opposites (negative counterparts), and zero. They are distinct from fractions, decimals, and percents. An integer can be a zero, a positive, or a negative whole number. The set of integers is denoted mathematically as {…, -3, -2, -1, 0, 1, 2, 3}. These numbers form the backbone of many mathematical operations and concepts, especially in algebra.

Positive and Negative Integers

Positive and negative integers make understanding and calculating many real-world situations better and more efficient.

Positive integers , often natural numbers , are numbers greater than zero. They are frequently used to denote weight, distance, or money values. However, not all situations can be expressed with positive numbers; sometimes, we must resort to negative ones.

Negative integers are the opposites of natural numbers, excluding zero, and fall below zero on the number line. They are typically used when something is decreased, removed, or lost. An excellent example of using negative integers is in banking, where they represent debt. Or in meteorology, where they represent temperatures below zero.

Understanding the concept of positive and negative integers is paramount because they are central to successfully dealing with integer word problems. In the next segment, we will dive deeper into strategies for solving these problems, so tighten your seatbelts as we explore a fun section of the mathematical world.

Addition and Subtraction Word Problems

When it comes to integers, understanding how to add and subtract these numbers is crucial, taking center stage in everyday mathematical operations. While learning, students begin grappling with word problems – mathematical problems presented in the form of a narrative or story – which include real-world scenarios. These serve as a bridge for children and adults to apply theoretical knowledge practically.

Adding and Subtracting Integers

In terms of  adding integers , there are a few rules to remember. If the integers have the same sign, add their absolute values and keep the standard sign. On the flip side, when the integers have different signs, subtract the smaller absolute value from the larger one and give the solution the sign of the number with the more considerable absolute value.

Subtracting integers , however, involves an additional step. More specifically, any subtraction can be reinterpreted as an addition. To subtract an integer, add its opposite. For example, to subtract -3 from 5 (5 – -3), we add 3 to 5 (5 + 3), with the sum coming to 8.

Real-life Examples of Addition and Subtraction Word Problems

Let’s explore a few word problems that imitate daily life scenarios. Suppose a child has £5 and they want to buy a toy that costs £10. How many more pounds do they need? The problem here is 10 – 5, which equals 5. Thus, the child needs five more pounds.

In another situation, imagine the temperature was 5 degrees Celsius in the morning and dropped 3 degrees by the afternoon. What’s the temperature now? Here, we have 5 – 3 = 2. The answer is 2 degrees Celsius.

These examples illustrate how adding and subtracting integers can help us solve practical problems and better understand the world. We encourage you to find your examples and practice to enhance your understanding and mastery of this fundamental mathematical skill.

Multiplication and Division Word Problems

As the journey of discovery with integers continues, multiplication and division of these numbers become an integral part of our everyday mathematical activities. Understanding how to tackle word problems – mathematical problems in narrative form – becomes critical. Specifically, multiplication and division integer word problems provide the groundwork for applying knowledge practically in real-world situations.

Multiplying and Dividing Integers

Multiplying integers might initially seem complex , but it becomes straightforward once you grasp the core concept. When multiplying two integers, the result will be positive if the signs are the same (positive or negative). However, if the signs are different (positive and negative), the result will be a negative integer.

Dividing integers  follows a similar concept. If the integers have the same sign, the quotient is positive, and if they have different signs, it is negative.

Application of Multiplication and Division Word Problems

Now, let’s see how these concepts apply in real-world scenarios. Suppose a person has $20 and wants to buy as many chocolates as possible, with each chocolate bar costing $4. In this case, they’d need to divide 20 by 4. The question boils down to 20 ÷ 4, which equals 5. So, they can buy five chocolate bars.

Considering multiplication, imagine a scenario where a store sells packages of bottled drinking water. Each package contains six bottles, and the store has twenty packages. To calculate the total number of bottles, you would multiply 6 (bottles per package) by 20 (number of packages), getting 6 x 20 = 120. So, the store has 120 bottled water.

These real-world examples show how multiplication and division word problems offer practical ways to understand and apply mathematical knowledge. Engaging with these problems enhances understanding of fundamental math concepts and promotes problem-solving skills crucial for daily life.

Multi-Step Word Problems

In a journey through mathematics, we commonly encounter complex multi-step word problems. These problems often involve multiple operations using integers , such as addition, subtraction, multiplication, and division. Solving these tasks enhances problem-solving skills, logical thinking, and mathematical proficiency. This part will delve into complex integer word problems and introduce strategies for solving multi-step problems.

Complex Integer Word Problems

Complex integer word problems  involve more than one mathematical operation, often requiring a systematic approach to reach the solution. For instance, imagine a scenario where a garden filled with 120 roses and petunias is being prepared for a garden show. There are twice as many roses as there are petunias. The question is, “How many petunias are there?”

Here, the problem will be solved in two steps. First, understanding that the number of roses is twice that of petunias. That means, if we denote the number of petunias as ‘p,’ then the number of roses is ‘2p’. The total quantity of flowers (120) is the sum of roses and petunias, leading to the equation 2p + p = 120. Solving this equation provides the number of petunias. Since multi-step word problems rely heavily on integers, understanding their operation rules is essential.

Strategies for Solving Multi-Step Word Problems

Solving multi-step word problems  can seem daunting, but a systematic approach simplifies the task. Below are vital strategies:

• Understand the Problem:  Read the problem carefully, ensure you understand what it’s asking, and identify the operations needed.
• Develop a Plan:  Break down the problem into smaller, manageable steps. Form equations if needed.
• Solve:  Carry out each operation. Ensure your calculations are correct at each step.
• Check Your Answer:  Review your solution, ensuring you answered the initial question correctly. Doing this validates that your solution aligns with the problem’s conditions.

Remember, practice significantly improves problem-solving skills and the ability to tackle complex multi-step word problems involving integers. Happy problem-solving!

Common Mistakes and Tips for Success

In particular, integer word problems can sometimes throw you off course. Like every journey, it is customary to make mistakes along the way. However, understanding and learning from these common errors can help you avoid detours and get you on the fast track to mastery.

Common Errors in Solving Integer Word Problems

Misinterpretation  is one of the most common mistakes when handling integer word problems. Often, students need to understand the operations required or interpret the relationship between the integers presented in the problem.

Inaccurate Calculations  – Integers include both positive and negative numbers, and it is easy to miscalculate when it comes to subtraction, addition, or other operations involving such numbers. For example, subtracting a negative integer leads to an addition instead.

Helpful Tips and Tricks for Solving Integer Word Problems

Once you’re aware of common pitfalls, arm yourself with the right strategies to navigate your way through complex integer word problems adeptly.

Thorough Understanding:  Read the integer word problem carefully and understand what is being asked. It can be helpful to jot down essential information or even draw diagrams to visualize the problem.

Plan:  Make a plan. Break the problem down into smaller, solvable parts and create equations representing each step of the problem.

Check Your Work:  After solving, double-check your calculations to ensure accuracy. Compare your answer with the original question to see if it makes sense.

Practice:  Just like anything, practice makes perfect. The more problems you solve, the more comfortable you become with integers and their operations.

Always remember making mistakes is part of the learning process. By staying aware and utilizing strategies, you’ll soon find yourself an expert at solving integer word problems. Happy Practicing!

Practice Exercises

Knowing the common errors and tips for solving integer word problems, it is time to put that knowledge into practice. With the right amount of practice, anyone can enhance their skills in solving such problems. With that in mind, let’s tackle some practice exercises to understand integer word problems further.

Practice Problems for Integer Word Problems

Here are some various types of integer word problems. Remember to read carefully, understand what’s asked, and plan your solution before jumping into the problem.

• Maria has $15 in her pocket. She spends $7 on a movie and $6 on snacks. Write an integer to represent Maria’s money situation and calculate how much she has left.
• At the start of the week, the temperature is 5 degrees. The temperature then drops by 7 degrees the next day. What is the temperature now?
• A company lost $2000 this year, 3 times the amount they lost last year. How much did the company lose last year?

Step-by-Step Solutions for Practice Exercises

Let’s walk through the solutions together to help you understand how these problems are solved.

• Maria has $15. She spent $7 and $6. This expenditure is a loss, so we represent it with negative integers. So, the situation becomes: 15 + (-7) + (-6) = 2. Maria has $2 left.
• The temperature is 5 degrees initially. Then, it drops by 7 degrees (a decrease is a negative operation). So, the situation is 5 + (-7) = -2 degrees. The temperature is now -2 degrees.
• Let’s denote the amount of money the company lost last year as x. We know that 3x = $2000. So, x = $2000 / 3 = $666.67. The company lost around $666.67 last year.

Do more exercises and get comfortable with solving integer word problems. It may take some time, but you will get there with consistent practice. Remember, avoiding rushing and breaking the problem into smaller parts can be very helpful. Practicing will make you better at solving integer word problems effectively and efficiently. Happy learning!

Emerging victorious in integer word problems opens up an exciting facet of mathematical knowledge. After all, these problems translate mathematical concepts into real-world scenarios, thereby cultivating critical thinking skills. Let’s explore the benefits of mastering integer word problems and round off with a few parting thoughts.

Benefits of Mastering Integer Word Problems

Boosts Problem-solving Skills:  Integer word problems are an ideal way to sharpen problem-solving skills. They compel one to think logically and systematically about how to apply mathematical operations accurately.

Enhances Numerical Literacy: With a firm grasp of integers, people can better comprehend numerical information daily. For instance, understanding debt and assets or gain and loss in finance becomes clearer.

Encourages Diversity of Thought:  Integer word problems offer multiple ways to find a solution, fostering creativity. It encourages diverse approaches to problem-solving.

Promotes Practical Application:  Integers have ubiquitous applications in diverse fields, including science, engineering, and information technology. Being comfortable with integer word problems equips one with skills applicable to these areas.

Final Thoughts on Integer Word Problems

Integer word problems seem daunting initially, but their mastery is a matter of regular practice and strategy. Break down the problem, identify what operation is warranted, and then move towards a solution progressively. Remember to cross-check the answer, as it ensures correctness.

Remember, it’s perfectly fine to make mistakes while learning. They are merely stepping stones to success. So, stay patient, persist in your efforts, and remember the tips shared. You will soon gain a commendable prowess over integer word problems. The confidence and skills you gain here will be beneficial throughout your mathematical journey.

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Integers Worksheets

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• Math Article
• Word Problems On Integers

Integers: Word Problems On Integers

An arithmetic operation is an elementary branch of mathematics. Arithmetical operations include addition, subtraction, multiplication and division. Arithmetic operations are applicable to different types of numbers including integers.

Integers are a special group of numbers that do not have a fractional or a decimal part. It includes positive numbers, negative numbers and zero.  Arithmetic operations on integers are similar to that of whole numbers. Since integers can be positive or negative numbers i.e. as these numbers are preceded either by a positive (+) or a negative sign (-), it makes them a little confusing concept. Therefore, they are different from whole numbers . Let us now see how various arithmetical operations can be performed on integers with the help of a few word problems. Solve the following word problems using various rules of operations of integers.

Word problems on integers Examples:

Example 1: Shyak has overdrawn his checking account by Rs.38.  The bank debited him Rs.20 for an overdraft fee.  Later, he deposited Rs.150.  What is his current balance?

Solution:  Given,

Total amount deposited= Rs. 150

Amount overdrew by Shyak= Rs. 38

Amount charged by bank= Rs. 20

⇒ Debit amount= -20

Total amount debited = (-38) + (-20) = -58

Current balance= Total deposit +Total Debit

Hence, the current balance is Rs. 92.

Example 2: Anna is a microbiology student. She was doing research on optimum temperature for the survival of different strains of bacteria. Studies showed that bacteria X need optimum temperature of -31˚C while bacteria Y need optimum temperature of -56˚C. What is the temperature difference?

Solution: Given,

Optimum temperature for bacteria X = -31˚C

Optimum temperature for bacteria Y= -56˚C

Temperature difference= Optimum temperature for bacteria X – Optimum temperature for bacteria Y

⇒ (-31) – (-56)

Hence, temperature difference is 25˚C.

Example 3: A submarine submerges at the rate of 5 m/min. If it descends from 20 m above the sea level, how long will it take to reach 250 m below sea level?

Initial position = 20 m    (above sea level)

Final position = 250 m    (below sea level)

Total depth it submerged = (250+20) = 270 m

Thus, the submarine travelled 270 m below sea level.

Time taken to submerge 1 meter = 1/5 minutes

Time taken to submerge 270 m = 270 (1/5) = 54 min

Hence, the submarine will reach 250 m below sea level in 54 minutes.

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6th Grade Integers Worksheets

6th grade integers worksheets give students a better understanding of how to work with integers. These worksheets incorporate questions based on applying arithmetic operators to integers, representing them on a number line, and word problems based on this concept.

Benefits of 6th Grade Math Worksheets Integers

Integers from a topic that is integral to understanding the number system. Hence, students must be well versed in this topic. 6th grade integers worksheets consist of several questions that enable children to get rid of any confusion they might have regarding the topic. As these questions are arranged in a well-structured manner, students find it easy to navigate through the sums. These 6th grade math worksheets also include answer keys that can be used by kids in case of any doubts.

Printable PDFs for Integers 6th Grade Worksheets

The integers grade 6 worksheets is free to download, easy to use, and is provided with several visual simulations for the benefit of the student.

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Division of Integers Exercises

Dividing integers practice problems with answers.

There are ten (10) practice questions below about dividing integers . Keep practicing until you master the skill! Good luck!

For your convenience, I included a summary on how to divide integers. The main idea is that if you divide two integers with the same sign , the answer is positive . However, if the signs of the two integers are different , the answer is negative .

Problem 1: Divide the integers: [latex]21 \div 7[/latex]

[latex]3[/latex]

Problem 2: Divide the integers: [latex]\left( { – 42} \right) \div 6[/latex]

[latex]-7[/latex]

Problem 3: Divide the integers: [latex]36 \div \left( { – 4} \right)[/latex]

[latex]-9[/latex]

Problem 4: Divide the integers: [latex]\left( { – 54} \right) \div \left( { – 9} \right)[/latex]

[latex]6[/latex]

Problem 5: Divide the integers: [latex]\left( { – 144} \right) \div 6[/latex]

[latex]-24[/latex]

Problem 6: Divide the integers: [latex]\left( { – 19} \right) \div \left( { – 19} \right)[/latex]

[latex]1[/latex]

Problem 7: Divide the integers: [latex]132 \div 12[/latex]

[latex]11[/latex]

Problem 8: Divide the integers: [latex]189 \div \left( { – 9} \right) \div \left( { – 7} \right)[/latex]

Problem 9: Divide the integers: [latex]120 \div \left( { – 2} \right) \div 5[/latex]

[latex]-12[/latex]

Problem 10: Divide the integers: [latex]\left( { – 96} \right) \div \left( { – 4} \right) \div \left( { – 6} \right)[/latex]

[latex]-4[/latex]

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• Word Problems on Integers

Understanding Integers

For solving integer word problems students need the right base of knowledge on integers. Proper practice is required for solving integer questions correctly. In this article, we will help students develop the base required for answering word problems on integers for Class 7.

Let’s start with the fact that an arithmetic operation is an elementary branch of mathematics. Arithmetic operations are subtraction, addition, division, and multiplication. These arithmetic operations are used for solving integer problems. There are also other types of numbers that can be solved with the help of arithmetic operations.

It should also be noted that integers are a special group that does not contain any decimal or fractional part. Integers include positive numbers, negative numbers, and zero . Also, arithmetic operations on integers are similar to whole numbers .

It also makes it a little confusing to solve word problems on integers for class 6 and word problems on integers for class 7 pdf because there are both positive and negative numbers. This is also why integers are different from whole numbers.

Integers can also be plotted on a number line. A number line might also be used by students when learning how to solve integers questions. These types of questions are more common when it comes to integers word problems Class 7. If you have never seen a number line, then an image of a number line is attached below.

Rules of Integers 

There are several rules that students need for learning how to solve integer word problems. Some of those rules are mentioned below.

The sum of any two positive integers will result in an integer.

The sum of any two negative integers is an integer.

The product of two positive integers will give an integer.

The product of two negative integers will be given an integer.

The sum of any integer and its inverse will be equal to zero.

The product of an integer and its reciprocal will be equal to 1.

Now, let’s look at addition, multiplication, subtraction, and division of signed integer numbers. This will help students to work on story problems with integers answer key.

The Addition of Signed Integer Numbers

As mentioned above, if we add two integers with the same sign, then we have to add the absolute value along with the sign that was provided with the number. For example, (+4) + (+7) = +11 and (-6) + (-4) = -10.

Also, if we add two integers with different signs, then we have to subtract the absolute values and write down the difference. This should be done with the sign of the number that has the largest absolute value. For example, (-4) + (+2) = -2 and (+6) + (-4) = +2.

Subtraction of Signed Integer Numbers

If a student wants to solve integer example problems, then he or she needs to know that while subtracting two integers, we have to change the sign of the second number. The second number should be subtracted and the rules of addition should also be followed. For example, (-7) - (+4) = (-7) + (-4) = -11 and (+8) - (+3) = (+8) + (-3) = +5.

Multiplication and Division of Signed Integer Numbers

When it comes to working on integer word problems with solutions of multiplying and dividing two integer numbers, then the rules are quite straightforward. If both the integers have the same sign, then the final results are positive. If the integers have different signs, then the final result is negative. For example, (+2) x (+3) = +6, (+3) x (-4) = -12, (+6) / (+2) = +3, and (-16) / (+4) = -4.

Properties of Integers

Students should also be familiar with the properties of integers if they want to work on integer word problems grade 6 with solutions. Some of those properties of integers are:

Closure property

Associative property

Commutative property

Distributive property

Additive inverse property

Multiplicative inverse property

Identity property

We also need to look at these properties in detail for solving integer problems in 6th grade. Let’s move on to that discussion.

Closure Property:

According to the closure property of integers, if two integers are added or multiplied together, the final result will be an integer only. This means that if a and b are integers, then:

a + b = integer

a x b = integer

For example, 2 + 5 = 7, which is an integer, and 2 x 5 = 10, which is also an integer.

Commutative Property:

According to this property, if a and b are two integers, then a + b = b + a and a x b = b x a. For example, 3 + 8 = 8 x 3 = 24 and 3 + 8 = 8 + 3 = 11. It should be noted that this property is not followed in the case of subtraction and division.

According to the associative property, if a, b, and c are integers, then:

a + (b + c) = (a + b) + c

a x (b x c) = (a x b) x c

For example, 2 + (3 + 4) = (2 + 3) + 4 = 9 and 2 x (3 x 4) = (2 x 3) x 4 = 24.

This property is only valid when it comes to addition and multiplication.

Distributive Property:

The distributive property states that if a, b, and c are integers, then a x (b + c) = a x b + a x c. For example, if we have to prove that 3 x (5 +1) = 3 x 5 + 3 x 1, then we should be start by finding:

LHS = 3 x (5 + 1) = 3 x 6 = 18

RHS = 3 x 5 + 3 x 1 = 15 + 3 = 18

Since, LHS = RHS

This proves our example.

Additive Inverse Property:

This additive inverse property states that if a is an integer, then a + (-a) = 0. This means that-a is the additive inverse of integer a.

Multiplicative Inverse Property:

The multiplicative inverse property states that if a is an integer, then a x (1 / a) = 1. This  means that 1 / a is the multiplicative inverse of integer a.

Identity Property of Integers:

The identity property of integers states that a + 0 = a and a x 1 = a. For example, 4 + 0 = 4 and 4 x 1 = 4.

Types of Integers

Earlier, we mentioned that there are three types of integers. In this section, we will look at these types of integers in more depth. The list of those types of integers is mentioned below.

Zero can be characterized as neither a positive nor a negative integer. It can be best defined as a neutral number. This also refers to the fact that zero has no sign (+ or -).

Positive Integers:

As the name indicates, positive integers are those numbers that are positive in their nature. These numbers are represented by a positive or plus (+) sign. The positive integers lie on the right side of the zero on the number line. This also means that all positive integers are greater than zero. For example, 122, 54, and 9087268292.

Negative Integers:

Negative integers, on the other hand, are numbers that are represented by a minus (-) or negative sign. These numbers are present on the left side of the zero on a number line. For example, -182, -8292, and -2927225.

Fun Facts About Integers

The word integer comes from the Latin word “ integer ” which literally means whole. 

You might find it interesting to note that integers are not just simple numbers on paper. Instead, these numbers have real-life applications! Both positive and negative integers are used to symbolize two contradicting situations in the real world. For example, if the temperature is above zero, then positive integers are used for denoting the temperature. But if the temperature is less than zero, then negative integers are used for denoting the temperature.

Integers can also help an individual in comparing and measuring two things like how small or big or few or more things are. These integers help in quantifying things. For example, in games like cricket and soccer, integers are used for keeping a track of scores. Movies and songs can also be rated by using integers!

FAQs on Word Problems on Integers

1. What are integers and what is their importance? 

An integer is usually defined as a number that can be written without any type of fractional component. These numbers tend to consist of zero, positive natural numbers or whole numbers, and their additive inverses. For example, 2, -56, 98, -302, etc. A set of integers is always denoted by the letter “Z”. 

The concept of integers is quite an important one to learn in mathematics. This is mainly because integers tend to help us compute the efficiency in both negative as well as positive numbers in a wide range of fields. They also help us to facilitate a number of calculations that are imperative to our daily lives. For example, we use integers to describe the temperature above or below the freezing point, to debit or credit money, etc. 

2. What are the rules for adding and subtracting integers?

There are some rules to be noted while adding two or more integers. They are as follows: 

The sum of an integer and its additive inverse is always zero. 

When you add two positive integers, the result will always be a positive number which will be greater than the two integers. 

When you add two negative integers, the result will always be a negative number which will be smaller than the two integers you added.

By finding the difference between the absolute value of a positive integer and a negative one, you can add both of them. And the sign of the greater number out of the two will be attached to the end product. 

When you add an integer with zero, you will get the same number as the answer. 

There are some rules to be noted while subtracting two or more integers. They are as follows: 

When you subtract any integer from zero, the answer will be either the additive inverse or the opposite of the integer. And when you subtract zero from any integer, then the result will always be the integer itself. 

If you want to subtract two integers that have the same sign, you ought to perform a subtraction operation on the absolute values of those numbers. 

If you want to subtract two integers that have different signs, you ought to add the absolute values. 

3. State the principles that the addition and subtraction of integers on a number line is based on. 

The principles upon which the addition of integers on a number line is based are as follows: 

Moving towards the right or the positive side of the number line will lead to the addition of a positive integer. 

Moving towards the left or the negative side of the number line will lead to the addition of a negative integer. 

Any of the integers can be taken as the base point (the point from where you start to move on the number line). 

The principles upon which the subtraction of integers on a number line is based are as follows: 

Every subtraction fact can also be written as an addition fact. 

Moving towards the left or the negative side of the number line will lead to the subtraction of a positive integer. 

Moving towards the right or the positive side of the number line will lead to the subtraction of a negative integer. 

4. Is multiplying rational numbers just like multiplying integers? If so, how?

To a certain extent, multiplying rational numbers is just like multiplying integers because the rules that are applicable to the latter, are also the same for the former. Rational numbers are just numbers that can be written in the fraction form of two given integers. So, if both the divisor and the dividend have the same signs, then the quotient will be positive. And if the divisor and the dividend have different signs, then the quotient will be negative. 

5. Can integers be decimals?

No. Just like whole numbers, integers can neither be fractions, nor can they be decimals. All integers can be expressed as a decimal, however, most of the numbers that are decimals cannot be expressed as integers. If there are any digits after the decimal point, and all of them are zeroes, only then can the number be identified as an integer. 

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