problem solving involving subtraction of whole numbers

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1.5: Subtraction of Whole Numbers

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• Page ID 48778

• Denny Burzynski & Wade Ellis, Jr.
• College of Southern Nevada via OpenStax CNX

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Learning Objectives

• understand the subtraction process
• be able to subtract whole numbers
• be able to use a calculator to subtract one whole number from another whole number

Subtraction

Definition: Subtraction

Subtraction is the process of determining the remainder when part of the total is removed.

Suppose the sum of two whole numbers is 11, and from 11 we remove 4. Using the number line to help our visualization, we see that if we are located at 11 and move 4 units to the left, and thus remove 4 units, we will be located at 7. Thus, 7 units remain when we remove 4 units from 11 units.

Definition: The Minus Symbol

The minus symbol (-) is used to indicate subtraction. For example, 11 − 4 indicates that 4 is to be subtracted from 11.

Definition: Minuend

The number immediately in front of or the minus symbol is called the minuend , and it represents the original number of units.

Definition: Subtrahend

The number immediately following or below the minus symbol is called the subtrahend , and it represents the number of units to be removed .

Definition: Difference

The result of the subtraction is called the difference of the two numbers. For example, in 11 − 4 = 7

Subtraction as the Opposite of Addition

Subtraction can be thought of as the opposite of addition. We show this in the problems in Sample Set A.

Sample Set A

8 - 5 = 3 since 3 + 5 = 8.

9 - 3 = 6 since 6 + 3 = 9.

Practice Set A

Complete the following statements.

7 - 5 = since + 5 = 7

7 - 5 = 2 since 2 + 5 = 7

9 - 1 = since + 1 = 9

9 - 1 = 8 since 8 + 1 = 9

17 - 8 = since + 8 = 17

17 - 8 = 9 since 9 + 8 = 17

The Subtraction Process

We'll study the process of the subtraction of two whole numbers by considering the difference between 48 and 35.

which we write as 13.

The Process of Subtracting Whole Numbers

To subtract two whole numbers,

The process

• Write the numbers vertically, placing corresponding positions in the same column. \(\begin{array} {r} {48} \\ {\underline{-35}} \end{array}\)
• Subtract the digits in each column. Start at the right, in the ones position, and move to the left, placing the difference at the bottom. \(\begin{array} {r} {48} \\ {\underline{-35}} \\ {13} \end{array}\)

Sample Set B

Perform the following subtractions.

\(\begin{array} {r} {275} \\ {\underline{-142}} \\ {133} \end{array}\)

\(\begin{array} {l} {5 - 2 = 3.} \\ {7 - 4 = 3.} \\ {2 - 1 = 1.} \end{array}\)

\(\begin{array} {r} {46,042} \\ {\underline{-\ \ 1,031}} \\ {45,011} \end{array}\)

\(\begin{array} {l} {2 - 1 = 1.} \\ {4 - 3 = 1.} \\ {0 - 0 = 0.} \\ {6 - 1 = 5.} \\ {4 - 0 = 4.} \end{array}\)

Find the difference between 977 and 235.

Write the numbers vertically, placing the larger number on top. Line up the columns properly.

\(\begin{array} {r} {977} \\ {\underline{-235}} \\ {742} \end{array}\)

The difference between 977 and 235 is 742.

In Keys County in 1987, there were 809 cable television installations. In Flags County in 1987, there were 1,159 cable television installations. How many more cable television installations were there in Flags County than in Keys County in 1987?

We need to determine the difference between 1,159 and 809.

There were 350 more cable television installations in Flags County than in Keys County in 1987.

Practice Set B

\(\begin{array} {r} {534} \\ {\underline{-203}} \end{array}\)

\(\begin{array} {r} {857} \\ {\underline{-\ \ 43}} \end{array}\)

\(\begin{array} {r} {95,628} \\ {\underline{-34,510}} \end{array}\)

\(\begin{array} {r} {11,005} \\ {\underline{-\ \ 1,005}} \end{array}\)

Find the difference between 88,526 and 26,412.

In each of these problems, each bottom digit is less than the corresponding top digit. This may not always be the case. We will examine the case where the bottom digit is greater than the corresponding top digit in the next section.

Subtraction Involving Borrowing

Definition: Minuend and Subtrahend

It often happens in the subtraction of two whole numbers that a digit in the minuend (top number) will be less than the digit in the same position in the subtrahend (bottom number). This happens when we subtract 27 from 84.

\(\begin{array} {r} {84} \\ {\underline{-27}} \end{array}\)

We do not have a name for 4 − 7. We need to rename 84 in order to continue. We'll do so as follows:

Our new name for 84 is 7 tens + 14 ones.

Notice that we converted 8 tens to 7 tens + 1 ten, and then we converted the 1 ten to 10 ones. We then had 14 ones and were able to perform the subtraction.

Definition: Borrowing

The process of borrowing (converting) is illustrated in the problems of Sample Set C.

Sample Set C

• Borrow 1 ten from the 8 tens. This leaves 7 tens.
• Convert the 1 ten to 10 ones.
• Add 10 ones to 4 ones to get 14 ones.

• Borrow 1 hundred from the 6 hundreds. This leaves 5 hundreds.
• Convert the 1 hundred to 10 tens.
• Add 10 tens to 7 tens to get 17 tens.

Practice Set C

Perform the following subtractions. Show the expanded form for the first three problems.

\(\begin{array} {r} {53} \\ {\underline{-35}} \end{array}\)

\(\begin{array} {r} {76} \\ {\underline{-28}} \end{array}\)

\(\begin{array} {r} {872} \\ {\underline{-565}} \end{array}\)

\(\begin{array} {r} {441} \\ {\underline{-356}} \end{array}\)

\(\begin{array} {r} {775} \\ {\underline{-\ \ 66}} \end{array}\)

\(\begin{array} {r} {5,663} \\ {\underline{-2,559}} \end{array}\)

Borrowing More Than Once

Sometimes it is necessary to borrow more than once . This is shown in the problems in Sample Set D.

Sample Set D

Perform the Subtractions. Borrowing more than once if necessary

• Borrow 1 ten from the 4 tens. This leaves 3 tens.
• Add 10 ones to 1 one to get 11 ones. We can now perform 11 − 8.
• Add 10 tens to 3 tens to get 13 tens.
• Now 13 − 5 = 8.
• 5 − 3 = 2.

• Borrow 1 ten from the 3 tens. This leaves 2 tens.
• Add 10 ones to 4 ones to get 14 ones. We can now perform 14 − 5.
• Borrow 1 hundred from the 5 hundreds. This leaves 4 hundreds.
• Add 10 tens to 2 tens to get 12 tens. We can now perform 12 − 8 = 4.
• Finally, 4 − 0 = 4.

\(\begin{array} {r} {71529} \\ {\underline{-\ \ 6952}} \end{array}\)

After borrowing, we have

Practice Set D

\(\begin{array} {r} {526} \\ {\underline{-358}} \end{array}\)

\(\begin{array} {r} {63,419} \\ {\underline{-\ \ 7,779}} \end{array}\)

\(\begin{array} {r} {4,312} \\ {\underline{-3,123}} \end{array}\)

Borrowing from Zero

It often happens in a subtraction problem that we have to borrow from one or more zeros. This occurs in problems such as

\(\begin{array} {r} {503} \\ {\underline{-\ \ 37}} \\ {\text{and}\ \ \ \ } \\ {5000} \\ {\underline{-\ \ \ \ 37}} \end{array}\)

We'll examine each case.

Borrowing from a single zero.

Consider the problem \(\begin{array} {r} {503} \\ {\underline{-\ \ 37}} \end{array}\)

Since we do not have a name for 3 − 7, we must borrow from 0.

Since there are no tens to borrow, we must borrow 1 hundred. One hundred = 10 tens.

We can now borrow 1 ten from 10 tens (leaving 9 tens). One ten = 10 ones and 10 ones + 3 ones = 13 ones.

Now we can suggest the following method for borrowing from a single zero.

Borrowing from a Single Zero To borrow from a single zero,

• Decrease the digit to the immediate left of zero by one.
• Draw a line through the zero and make it a 10.
• Proceed to subtract as usual.

Sample Set E

Perform this subtraction.

\(\begin{array} {r} {503} \\ {\underline{-\ \ 37}} \end{array}\)

The number 503 contains a single zero

Practice Set E

Perform each subtraction.

\(\begin{array} {r} {906} \\ {\underline{-\ \ 18}} \end{array}\)

\(\begin{array} {r} {5102} \\ {\underline{-\ \ 559}} \end{array}\)

\(\begin{array} {r} {9055} \\ {\underline{-\ \ 386}} \end{array}\)

Borrowing from a group of zeros

Consider the problem \(\begin{array} {r} {5000} \\ {\underline{-\ \ \ \ 37}} \end{array}\)

In this case, we have a group of zeros.

Since we cannot borrow any tens or hundreds, we must borrow 1 thousand. One thousand = 10 hundreds.

We can now borrow 1 hundred from 10 hundreds. One hundred = 10 tens.

We can now borrow 1 ten from 10 tens. One ten = 10 ones.

From observations made in this procedure we can suggest the following method for borrowing from a group of zeros.

Borrowing from a Group of zeros

To borrow from a group of zeros,

• Decrease the digit to the immediate left of the group of zeros by one.
• Draw a line through each zero in the group and make it a 9, except the rightmost zero, make it 10.

Sample Set F

\(\begin{array} {r} {40,000} \\ {\underline{-\ \ \ \ \ 125}} \end{array}\)

The number 40,000 contains a group of zeros.

• The number to the immediate left of the group is 4. Decrease 4 by 1. 4 - 1 = 3

Example \(\PageIndex{1}\)

\(\begin{array} {r} {8,000,006} \\ {\underline{-\ \ \ \ \ 41,107}} \end{array}\)

The number 8,000,006 contains a group of zeros.

• The number to the immediate left of the group is 8. Decrease 8 by 1. 8 - 1 = 7

Practice Set F

\(\begin{array} {r} {21,007} \\ {\underline{-\ \ 4,873}} \end{array}\)

\(\begin{array} {r} {10,004} \\ {\underline{-\ \ 5,165}} \end{array}\)

\(\begin{array} {r} {16,000,000} \\ {\underline{-\ \ \ \ \ 201,060}} \end{array}\)

Calculators

In practice, calculators are used to find the difference between two whole numbers.

Sample Set G

Find the difference between 1006 and 284.

The difference between 1006 and 284 is 722.

(What happens if you type 284 first and then 1006? We'll study such numbers in Chapter 10.)

Practice Set G

Use a calculator to find the difference between 7338 and 2809.

Use a calculator to find the difference between 31,060,001 and 8,591,774.

For the following problems, perform the subtractions. You may check each difference with a calculator.

Exercise \(\PageIndex{1}\)

\(\begin{array} {r} {15} \\ {\underline{-\ \ 8}} \end{array}\)

Exercise \(\PageIndex{2}\)

\(\begin{array} {r} {19} \\ {\underline{-\ \ 8}} \end{array}\)

Exercise \(\PageIndex{3}\)

\(\begin{array} {r} {11} \\ {\underline{-\ \ 5}} \end{array}\)

Exercise \(\PageIndex{4}\)

\(\begin{array} {r} {14} \\ {\underline{-\ \ 6}} \end{array}\)

Exercise \(\PageIndex{5}\)

\(\begin{array} {r} {12} \\ {\underline{-\ \ 9}} \end{array}\)

Exercise \(\PageIndex{6}\)

\(\begin{array} {r} {56} \\ {\underline{-12}} \end{array}\)

Exercise \(\PageIndex{7}\)

\(\begin{array} {r} {74} \\ {\underline{-33}} \end{array}\)

Exercise \(\PageIndex{8}\)

\(\begin{array} {r} {80} \\ {\underline{-61}} \end{array}\)

Exercise \(\PageIndex{9}\)

\(\begin{array} {r} {350} \\ {\underline{-141}} \end{array}\)

Exercise \(\PageIndex{10}\)

\(\begin{array} {r} {800} \\ {\underline{-650}} \end{array}\)

Exercise \(\PageIndex{11}\)

\(\begin{array} {r} {35,002} \\ {\underline{-14,001}} \end{array}\)

Exercise \(\PageIndex{12}\)

\(\begin{array} {r} {5,000,566} \\ {\underline{-2,441,326}} \end{array}\)

Exercise \(\PageIndex{13}\)

\(\begin{array} {r} {400,605} \\ {\underline{-121,352}} \end{array}\)

Exercise \(\PageIndex{14}\)

\(\begin{array} {r} {46,400} \\ {\underline{-\ \ 2,012}} \end{array}\)

Exercise \(\PageIndex{15}\)

\(\begin{array} {r} {77,893} \\ {\underline{-\ \ \ \ \ 421}} \end{array}\)

Exercise \(\PageIndex{16}\)

\(\begin{array} {r} {42} \\ {\underline{-18}} \end{array}\)

Exercise \(\PageIndex{17}\)

\(\begin{array} {r} {51} \\ {\underline{-27}} \end{array}\)

Exercise \(\PageIndex{18}\)

\(\begin{array} {r} {622} \\ {\underline{-\ \ 88}} \end{array}\)

Exercise \(\PageIndex{19}\)

\(\begin{array} {r} {261} \\ {\underline{-\ \ 73}} \end{array}\)

Exercise \(\PageIndex{20}\)

\(\begin{array} {r} {242} \\ {\underline{-158}} \end{array}\)

Exercise \(\PageIndex{21}\)

\(\begin{array} {r} {3,422} \\ {\underline{-1,045}} \end{array}\)

Exercise \(\PageIndex{22}\)

\(\begin{array} {r} {5,565} \\ {\underline{-3,985}} \end{array}\)

Exercise \(\PageIndex{23}\)

\(\begin{array} {r} {42,041} \\ {\underline{-15,355}} \end{array}\)

Exercise \(\PageIndex{24}\)

\(\begin{array} {r} {304,056} \\ {\underline{-\ \ 20,008}} \end{array}\)

Exercise \(\PageIndex{25}\)

\(\begin{array} {r} {64,000,002} \\ {\underline{-\ \ \ \ \ 856,743}} \end{array}\)

Exercise \(\PageIndex{26}\)

\(\begin{array} {r} {4,109} \\ {\underline{-\ \ \ 856}} \end{array}\)

Exercise \(\PageIndex{27}\)

\(\begin{array} {r} {10,113} \\ {\underline{-\ \ 2,079}} \end{array}\)

Exercise \(\PageIndex{28}\)

\(\begin{array} {r} {605} \\ {\underline{-\ \ 77}} \end{array}\)

\(\begin{array} {r} {59} \\ {\underline{-26}} \end{array}\)

\(\begin{array} {r} {36,107} \\ {\underline{-\ \ 8,314}} \end{array}\)

Exercise \(\PageIndex{29}\)

\(\begin{array} {r} {92,526,441,820} \\ {\underline{-59,914,805,253}} \end{array}\)

32,611,636,567

Exercise \(\PageIndex{30}\)

\(\begin{array} {r} {1,605} \\ {\underline{-\ \ 881}} \end{array}\)

Exercise \(\PageIndex{31}\)

\(\begin{array} {r} {30,000} \\ {\underline{-26,062}} \end{array}\)

Exercise \(\PageIndex{32}\)

\(\begin{array} {r} {600} \\ {\underline{-216}} \end{array}\)

Exercise \(\PageIndex{33}\)

\(\begin{array} {r} {90,000,003} \\ {\underline{-\ \ \ 726,048}} \end{array}\)

For the following problems, perform each subtraction.

Exercise \(\PageIndex{34}\)

Subtract 63 from 92.

The word "from" means "beginning at." Thus, 63 from 92 means beginning at 92, or 92 - 63.

Exercise \(\PageIndex{35}\)

Subtract 35 from 86.

Subtract 382 from 541.

Subtract 1,841 from 5,246.

Exercise \(\PageIndex{36}\)

Subtract 26,082 from 35,040.

Exercise \(\PageIndex{37}\)

Find the difference between 47 and 21.

Exercise \(\PageIndex{38}\)

Find the difference between 1,005 and 314.

Exercise \(\PageIndex{39}\)

Find the difference between 72,085 and 16.

Exercise \(\PageIndex{40}\)

Find the difference between 7,214 and 2,049.

Exercise \(\PageIndex{41}\)

Find the difference between 56,108 and 52,911.

Exercise \(\PageIndex{42}\)

How much bigger is 92 than 47?

Exercise \(\PageIndex{43}\)

How much bigger is 114 than 85?

Exercise \(\PageIndex{44}\)

How much bigger is 3,006 than 1,918?

Exercise \(\PageIndex{45}\)

How much bigger is 11,201 than 816?

Exercise \(\PageIndex{46}\)

How much bigger is 3,080,020 than 1,814,161?

Exercise \(\PageIndex{47}\)

In Wichita, Kansas, the sun shines about 74% of the time in July and about 59% of the time in November. How much more of the time (in per­cent) does the sun shine in July than in No­vember?

Exercise \(\PageIndex{48}\)

The lowest temperature on record in Concord, New Hampshire in May is 21°F, and in July it is 35°F. What is the difference in these lowest tem­peratures?

Exercise \(\PageIndex{49}\)

In 1980, there were 83,000 people arrested for prostitution and commercialized vice and 11,330,000 people arrested for driving while in­toxicated. How many more people were arrested for drunk driving than for prostitution?

Exercise \(\PageIndex{50}\)

In 1980, a person with a bachelor's degree in ac­counting received a monthly salary offer of $1,293, and a person with a marketing degree a monthly salary offer of $1,145. How much more was offered to the person with an accounting de­gree than the person with a marketing degree?

Exercise \(\PageIndex{51}\)

In 1970, there were about 793 people per square mile living in Puerto Rico, and 357 people per square mile living in Guam. How many more people per square mile were there in Puerto Rico than Guam?

Exercise \(\PageIndex{52}\)

The 1980 population of Singapore was 2,414,000 and the 1980 population of Sri Lanka was 14,850,000. How many more people lived in Sri Lanka than in Singapore in 1980?

Exercise \(\PageIndex{53}\)

In 1977, there were 7,234,000 hospitals in the United States and 64,421,000 in Mainland China. How many more hospitals were there in Mainland China than in the United States in 1977?

Exercise \(\PageIndex{54}\)

In 1978, there were 3,095,000 telephones in use in Poland and 4,292,000 in Switzerland. How many more telephones were in use in Switzerland than in Poland in 1978?

For the following problems, use the corresponding graphs to solve the problems.

Exercise \(\PageIndex{55}\)

How many more life scientists were there in 1974 than mathematicians?

Exercise \(\PageIndex{56}\)

How many more social, psychological, mathe­matical, and environmental scientists were there than life, physical, and computer scientists?

Exercise \(\PageIndex{57}\)

How many more prosecutions were there in 1978 than in 1974?

Exercise \(\PageIndex{58}\)

How many more prosecutions were there in 1976-1980 than in 1970-1975?

Exercise \(\PageIndex{59}\)

How many more dry holes were drilled in 1960 than in 1975?

Exercise \(\PageIndex{60}\)

How many more dry holes were drilled in 1960, 1965, and 1970 than in 1975, 1978 and 1979?

For the following problems, replace the ☐ with the whole number that will make the subtraction true.

Exercise \(\PageIndex{61}\)

\(\begin{array} {r} {14} \\ {\underline{-☐}} \\ {3} \end{array}\)

Exercise \(\PageIndex{62}\)

\(\begin{array} {r} {21} \\ {\underline{-☐}} \\ {14} \end{array}\)

Exercise \(\PageIndex{63}\)

\(\begin{array} {r} {35} \\ {\underline{-☐}} \\ {25} \end{array}\)

Exercise \(\PageIndex{64}\)

\(\begin{array} {r} {16} \\ {\underline{-☐}} \\ {9} \end{array}\)

Exercise \(\PageIndex{65}\)

\(\begin{array} {r} {28} \\ {\underline{-☐}} \\ {16} \end{array}\)

For the following problems, find the solutions.

Exercise \(\PageIndex{66}\)

Subtract 42 from the sum of 16 and 56.

Exercise \(\PageIndex{67}\)

Subtract 105 from the sum of 92 and 89.

Exercise \(\PageIndex{68}\)

Subtract 1,127 from the sum of 2,161 and 387.

Exercise \(\PageIndex{69}\)

Subtract 37 from the difference between 263 and 175.

Exercise \(\PageIndex{70}\)

Subtract 1,109 from the difference between 3,046 and 920.

Exercise \(\PageIndex{71}\)

Add the difference between 63 and 47 to the dif­ference between 55 and 11.

Exercise \(\PageIndex{72}\)

Add the difference between 815 and 298 to the difference between 2,204 and 1,016.

Exercise \(\PageIndex{73}\)

Subtract the difference between 78 and 43 from the sum of 111 and 89.

Exercise \(\PageIndex{74}\)

Subtract the difference between 18 and 7 from the sum of the differences between 42 and 13, and 81 and 16.

Exercise \(\PageIndex{75}\)

Find the difference between the differences of 343 and 96, and 521 and 488.

Exercises for Review

Exercise \(\PageIndex{76}\)

In the number 21,206, how many hundreds are there?

Exercise \(\PageIndex{77}\)

Write a three-digit number that has a zero in the ones position.

330 (answers may vary)

Exercise \(\PageIndex{78}\)

How many three-digit whole numbers are there?

Exercise \(\PageIndex{79}\)

Round 26,524,016 to the nearest million.

Exercise \(\PageIndex{80}\)

Find the sum of 846 + 221 + 116.

• Whole Numbers
• Addition & Subtraction Word Problems

Addition and Subtraction of Whole Numbers Word Problems Worksheets for Grade 6

Are your kids ready to practice their addition and subtraction skills with fun and challenging word problems? If they are, then you will love these addition and subtraction of whole numbers word problems worksheets for grade 6 !

They must use their logical thinking and problem-solving skills to find the answers. Some word problems are easy, but some are tricky and require multiple steps. Don't worry; you can do it! Just remember to check your answers.

These addition and subtraction of whole numbers word problems worksheets for grade 6 will help your kids master these math skills and prepare them for more advanced math topics.

GRADE 6 MATH TOPICS

• Whole numbers

Multiplication

• Exponents and square roots
• Number theory
• Add & subtract decimals
• Multiply & divide decimals
• Fractions & mixed numbers
• Add & subtract fractions
• Multiply fractions
• Divide fractions
• Operations with integers
• Mixed operations
• Rational numbers
• Problems solving
• Ratio & proportions
• Percentages
• Measuring units
• Consumer math
• Telling time
• Coordinate graph
• Algebraic expressions
• One step equations
• Solve & graph inequalities
• Two-step equations
• 2D Geometry
• Symmetry & transformation
• Geometry measurement
• Data and Graphs
• Probability

Grade 6 add & subtract whole numbers word problems worksheets

Click to download the worksheets:.

More of 6th Grade whole numbers worksheets pdf

Add and Subtract Whole Numbers Word Problems for Grade 6 with solutions and explanations

Here are 10 multiple-choice questions (MCQs) with four options each. Students can check their answers at the end of each worksheet.

• A library has 22,740 books in its collection. It lends out 5,219 books and receives 937 books as donations. How many books are left in the library after these transactions?
• A bakery sells 7,345 loaves of bread, 1,090 cupcakes, and 5,456 other pastries in a month. How many pastries did the bakery sell in all during the month?
• A factory produces 8,765 widgets in a week. It sells 6,543 widgets and discards 234 widgets as defective. How many widgets are left in the factory at the end of the week?
• A farmer has 123 cows and 456 sheep. He sells 78 cows and buys 45 sheep. How many cows and sheep does he have now?
• A store has 789 bottles of juice and 456 cans of soda. It sells 345 bottles of juice and 234 cans of soda in a day. How many bottles of juice and cans of soda are left in the store after a day?
• A family has a budget of $2,345 for a vacation. They spend $1,234 on transportation, $567 on accommodation, and $234 on food. How much money do they have left for other expenses?
• A museum receives 12,345 visitors per month. 3,987 of the visitors were adults, 5,067 were children over the age of 12, and the rest of the visitors were children under the age of 12. How many children under 12 visited the museum during the month?
• A box contains 123 chocolates of different flavors. There are 45 chocolates with caramel filling, 34 chocolates with nuts, and the rest are plain chocolates. How many plain chocolates are there in the box?
• A school bus can carry 56 students at a time. It makes three trips to pick up students from different locations and bring them to school. How many students can the bus pick up in total? How many students are left if there are 345 students who need to go to school?
• A company has a revenue of $12,345 in a month. It spends $5,678 on salaries, $2,345 on rent, $1,234 on utilities, and $567 on other expenses. How much profit or loss does the company make in a month?

Addition and subtraction of whole numbers word problems answers:

To find the number of books left in the library , we need to subtract the number of books lent out and add the number of books donated to the original collection.

The equation is 22,740 - 5,219 + 937 = 18,458.

Therefore, there are 18,458 books left in the library after these transactions.

To find the number of pastries sold by the bakery in a month , we need to add the number of loaves of bread, cupcakes, and other pastries.

The equation is 7,345 + 1,090 + 5,456 = 13,891.

Therefore, the bakery sold 13,891 pastries in all during the month.

To find the number of widgets left in the factory at the end of the week , we need to subtract the number of widgets sold and discarded from the number of widgets produced.

The equation is 8,765 - 6,543 - 234 = 1,988.

Therefore, there are 1,988 widgets left in the factory at the end of the week.

To find the number of cows and sheep that the farmer has now , we need to subtract the number of cows sold and add the number of sheep bought to the original numbers.

The equations are 123 - 78 = 45 and 456 + 45 = 501.

Therefore, the farmer has 45 cows and 501 sheep now.

To find the number of bottles of juice and cans of soda left in the store after a day , we need to subtract the number of bottles of juice and cans of soda sold from the original numbers.

The equations are 789 - 345 = 444 and 456 - 234 = 222.

Therefore, there are 444 bottles of juice and 222 cans of soda left in the store after a day.

To find out how much money the family has left for other expenses , we need to subtract the total amount they spend from their budget.

The total amount they spend is $1,234 + $567 + $234 = $2,035.

The amount they have left is $2,345 - $2,035 = $310. Therefore, the family has $310 left for other expenses.

To find out how many children under 12 visited the museum during the month , we need to subtract the number of adults and children over 12 from the total number of visitors.

The number of adults and children over 12 is 3,987 + 5,067 = 9,054.

The number of children under 12 is 12,345 - 9,054 = 3,291. Therefore, 3,291 children under 12 visited the museum during the month.

To find out how many plain chocolates are there in the box , we need to subtract the number of chocolates with caramel filling and nuts from the total number of chocolates.

The number of chocolates with caramel filling and nuts is 45 + 34 = 79.

The number of plain chocolates is 123 - 79 = 44.

Therefore, there are 44 plain chocolates in the box.

To find out how many students the bus can pick up in total , we need to multiply the number of students it can carry at a time by the number of trips it makes.

The number of students it can pick up in total is 56 + 56 + 56 = 168.

To find out how many students are left, we need to subtract the number of students it can pick up from the number of students who need to go to school.

The number of students who are left is 345 - 168 = 177.

Therefore, the bus can pick up 168 students in total, and there are 177 students left.

To find out how much profit or loss the company makes in a month , we need to subtract the total expenses from the revenue.

The total expenses are $5,678 + $2,345 + $1,234 + $567 = $9,824.

The profit or loss is $12,345 - $9,824 = $2,521.

Therefore, the company makes a profit of $2,521 in a month.

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WORD PROBLEMS INVOLVING OPERATIONS OF WHOLE NUMBERS

Problem 1 :

What number must be increased by 293 to get 648?

Let x be the required number.

What must be increased by  293  to get  648

x +  293  =  648

x = 648 - 293

Problem 2 :

A woman has $255 in her purse. She gives $35 to each of her five children. How much money does she have left?

Amount she has in her purse = $255

Each child gets = $35

Amount distributed :

Amount she has left :

= $255 - $175

Problem 3 :

The Year 8 students at a school are split into 4 equal classes of 27 students each. The school decides to increase the number of classes to 6. How many students will there be in each of the new classes, if the students are divided equally between them?

Number of existing classes = 4

Number of students in total :

Number of classes increased = 6

Number of students in each class :

=  ¹⁰⁸⁄₆

Problem 4 :

My bank account contains $3621 and I make monthly withdrawals of $78 for 12 months. What is my new bank balance.

My old balance = $3621

I make withfrawals $78 each month for 12 months.

Amount of withdrawal :

My new balance :

= old balance - withdrawal

= $3621 - $936

Problem 5 :

A contractor bought 34 loads of soil, each weighing 12 tonnes. If the soil cost $23 per tonne, what was the total cost ?

Number of loads = 34

Weight of 1 load = 12 tonnes

Cost of soil = $23 per tonne

Number of tonnes :

= 408 tonnes

Required cost :

=  $9384

Problem 6 :

4 less than three times of a whole number is equal to 8. Find the whole number. 

Let x be the required whole number.

From the given information,

Add 4 to both sides.

Divide both sides by 3.

The whole number is 4.

Problem 7 :

The sum of two whole numbers is 8 and that of the difference is 2. Find the two whole numbers.

Let x and y be the two required whole numbers such that x > y .

x + y = 8 ----(1)

x - y = 2 ----(2)

Add (1) and (2) :

Divide both sides by 2.

Substitute x = 5 into (1).

Subtract 5 from both sides.

The two whole numbers are 5 and 3.

Problem 8 :

In a two-digit whole number, the digit at the tens place is twice the digit at the ones place. If 18 is subtracted from it, the digits are reversed. Find the two-digit whole number.

Let x  be the digit in ones place.

Then the two-digit number is (2x)(x).

(2x)(x) - 18 = (x)(2x)

(10  ⋅  2x) + (1  ⋅ x) - 18 = (10 ⋅ x) + (1 ⋅ 2x)

20x + x - 18 = 10x + 2x

21x - 18 = 12x

Subtract 12x from both sides.

9x - 18 = 0

Add 18 to both sides.

The digit at the ones place is 2 and the digit at the tens place is 4.

So, the required two-digit number is 42.

Problem 9 :

A whole number consisting of two digits is four times the sum of its digits and if 27 be added to it, the digits are reversed. Find the whole number.

Let xy  be the required two-digit whole number.

Given : The two-digit whole is equal four times the sum of its digits

xy = 4(x + y)

(10  ⋅  x)  + (1 ⋅ y)  = 4x + 4y

10x + y = 4x + 4y

6x - 3y = 0

y = 2x ----(1)

Given : If 27 be added to it, the digits are reversed.

xy + 27 = yx

(10  ⋅ x) + (1 ⋅ y) + 27 = (10 ⋅ y) + (1 ⋅ x)

10 x + y + 27 = 10y + x

9x - 9y + 27 = 0

x - y + 3 = 0

Substitute y = 2x.

x - 2x + 3 = 0

Substitute x = 1 into (1).

Therefore, the required two-digit whole number is 36.

Problem 10 :

What are the smallest and largest three-digit whole numbers which are evenly divisible by 7?

Steps to find the smallest three-digit whole number divisible by 7 :

The smallest three-digit whole number is 100. Divide 100 by 7 and get the quotient and remainder.

When 100 is divided by 7, the quotient is 14 and the remainder is 2.

Subtract the remainder 2 from the divisor 7.

Add 5 to the dividend 100.

105 is the smallest three-digit number divisible by 7.

Steps to find the largest three-digit whole number divisible by 7 :

The largest three-digit whole number is 999. Divide 999 by 7 and get the quotient and remainder.

When 999 is divided by 7, the quotient is 142 and the remainder is 5.

Subtract the remainder 5 from the dividend 999.

994 is the largest three-digit number divisible by 7.

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Subtraction Word Problems (1-step word problems)

These lessons look at some examples of subtraction word problems that can be solved in one step, illustrating the use of bar models or block diagrams in the solution process.

Related Pages 2-step Subtraction Word Problems Using Bar Models Solving Word Problems Using Bar Models Singapore Math More Word Problems

We will illustrate how block diagrams can be used to help you to visualize the subtraction word problems in terms of the information given and the data that needs to be found. The block diagrams or block modeling method is used in Singapore Math.

Example: Jessica has 1135 beads. 604 beads are red and the rest are blue. How many blue beads does she have?

1135 – 604 = 531

She has 531 blue beads.

Example: James and Ken donated $2300 to a charitable organization. Ken donated $658. How much did James donate?

2300 – 658 = 1642 James donated $1642.

Example: The price of a car is $2795 and the price of a motorbike is $1063. What is the difference between the prices of the 2 vehicles?

Solution: 2795 – 1063 = 1732

The difference between the prices of the 2 vehicles is $1732.

Example: There are 967 chairs in a hall. During an event, 761 chairs were occupied. How many chairs were not occupied?

967 – 761 = 206 206 chairs were not occupied.

Examples of subtraction word problems

134 girls and 119 boys took part in an art competition. How many more girls than boys were there?

Mei Lin saved $184. She saved $63 more than Betty. How much did Betty saved?

John read 32 pages in the morning. He read 14 pages less in the afternoon. a) How many pages did he read in the afternoon? b) How many pages did they read altogether?

A visual way to solve world problems using bar modeling This type of word problem uses the part-whole model.

Example: Mr. Oliver bought 88 pencils. he sold 26 of them. How many pencils did he have left?

A visual way to solve world problems using bar modeling This type of word problem uses the part-whole model. Because the part is missing, this is a subtraction problem.

Example: There are 98 hats, 20 of them are pink and the rest are yellow. How many yellow hats are there?

Example: Cayla did 88 sit-ups in the morning. Nekira did 32 sit-ups at night. How many more sit-ups did Cayla do than Nekira?

How to use bar modeling in Singapore math to solve word problems that deal with comparing?

Example: Adam has 11 fewer lollipops than Hope. If Adam has 16 lollipops, how many lollipop does Hope have?

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Word Problems Involving Addition and Subtraction

Word problems involving addition and subtraction are discussed here step by step.

There are no magic rules to make problem solving easy, but a systematic approach can help to the problems easily. 

Word problems based on addition are broadly of two types: (a) When objects of two or more collections are put together.  For example:

Amy has 20 lemon sweets and 14 orange sweets. What is the total number of sweets Amy has?  (b) When an increase in number takes place. 

For example:

Victor has 14 stamps. His friend gave him 23 stamps. How many stamps does Victor have in all? The key words used in problems involving addition are:

s um; total; in all; all together.

Word problems based on subtraction are of several types: (a) Partitioning : Take away, remove, given away.

(b) Reducing : Find out how much has been given away or how much remains.

(c) Comparison : More than / less than.

(d) Inverse of addition : How much more to be added. The key words to look out for in a problem sum involving subtraction are: take away; how many more ; how many less ; how many left ; greater ; smaller.

1. The girls had 3 weeks to sell tickets for their play. In the first week, they sold 75 tickets. In the second week they sold 108 tickets and in the third week they sold 210 tickets. How may tickets did they sell in all? Tickets sold in the first week = 75

Tickets sold in the second week = 108

Tickets sold in the third week = 210

Total number of tickets sold = 75 + 108 + 210 = 393

Answer: 393 tickets were sold in all.

2. Mr. Bose spent $450 for petrol on Wednesday. He spent $125 more than that on Thursday. How much did he spend on petrol on those two days. This problem has to be solved in two steps.

Step 1: Money spent for petrol on Thursday

450 + 125 = $575 Step 2: Money spent for petrol on both days

450 + 575 = $1025

Examples on word problems on addition and subtraction:

1. What is the sum of 4373, 4191 and 3127? Solution: The numbers are arranged in columns and added.

Therefore, sum =11,691

2. What is the difference of 3867 and 1298?

Solution: The numbers are arranged in columns and subtracted:

Therefore, difference = 2569

3. Subtract 4358 from the sum of 5632 and 1324. Solution: Sum of 5632 and 1324

Difference of 6956 and 4358

Therefore, 2598 is the answer.

4. Find the number, which is

(i) 1240 greater than 3267.

(ii) 1353 smaller than 5292. Solution: (i) The number is 1240 more than 3267

Therefore, the number = 3267 + 1240 or = 4507 (ii) The number is 1353 less than 5292

= 5292 – 1353 or

5. The population of a town is 16732. If there are 9569 males then find the number of females in the town. Solution:

6. In a factory there are 35,675 workers. 10,750 workers come in the first shift, 12,650 workers in the second shift and the rest come in the third shift. How many workers come in the third shift? Solution: Number of workers coming in the first and second shift

= 10750 + 12650 = 23400

Therefore, number of workers coming in the third shift = 35675 - 23400 = 12275

Related Concept

● Word Problems on Addition

● Subtraction

● Check for Subtraction and Addition

● Word Problems Involving Addition and Subtraction

● Estimating Sums and Differences

● Find the Missing Digits

● Multiplication

● Multiply a Number by a 2-Digit Number

● Multiplication of a Number by a 3-Digit Number

● Multiply a Number

● Estimating Products

● Word Problems on Multiplication

● Multiplication and Division

● Terms Used in Division

● Division of Two-Digit by a One-Digit Numbers

● Division of Four-Digit by a One-Digit Numbers

● Division by 10 and 100 and 1000

● Dividing Numbers

● Estimating the Quotient

● Division by Two-Digit Numbers

● Word Problems on Division

4th Grade Math Activities From Word Problems Involving Addition and Subtraction to

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Subtraction word problems (1-3 digits)

Word problem worksheets: subtracting numbers below 1,000.

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Word Problems on Addition and Subtraction of Whole Numbers | Simple Addition and Subtraction Word Problems

Word Problems on Addition and Subtraction provided here covers different kinds of questions. Practice using the Addition and Subtraction Problems provided here and test where you stand in your preparation. Now we will see how to solve the word problems on addition and subtraction of whole numbers. Learn to apply the problem-solving approach used and try to solve related problems.

Also, Check:

• Combination of Addition and Subtraction
• Addition of Whole Numbers
• Subtraction of Whole Numbers

Addition and Subtraction of Whole Numbers Word Problems

Dany jogs 1200m and runs 1500 m. Find the total distance.

Solution: Given Dany jogs = 1200m Dany runs = 1500m Total distance covered by dany is = dany jogs + dany runs = 1200 + 1500 = 2700 m Therefore distance covered by dany is 2700 m

A book has 650 pages. Ted has read 220 pages so far. How many pages of this book are left to read by ted?

Given Number of pages in the book = 650 Number of pages read by ted = 220 Number of pages left to read by ted = Number of pages in the book – number of pages read by ted = 650 – 220 = 430 Therefore 430 pages are left to read by ted.

A factory makes 287 blue bags and 346 green bags in a month. How many bags does the factory produce in a month?

Solution: Given Number of blue bags = 287 Number of green bags = 346 Total number of bags = Number of blue bags + number of green bags = 287 + 346 = 633 Therefore factory produce 633 bags in the month,

Mary is the teacher of class first. She has 12 girls and 15 boys in her class. i)How many students are there in the class? ii)She has 30 boxes of crayons. How many more boxes of crayons are there than the number of students?

Given Number of girls = 12 Number of boys = 15 i)Total number of students = Number of girls + Number of boys = 12 + 15 = 27 Therefore, the total number of students in her class is 27 ii)Number of boxes mary have = 30 Number of boxes she needs = number of boxes mary have – total number of students = 30 – 27 = 3 Therefore, there are 3 more boxes of crayons than the number of students.

Jones bought a dozen pencils and erasers costing Rs.125.25 and Rs.110.06 respectively. She paid rs.500 to the shopkeeper. How much should she get back from the shopkeeper?

Given Cost of pencils = 125.25 Cost of erasers = 110.06 Total cost = cost of pencils + cost of erasers = 125.25 + 110.06 = 235.31rs Amount paid by jones to shopkeeper = 500.00 Total amount of pencils and erasers = 235.31 Difference = 500.00 – 235.31 = 264.69 Jones should get back rs 264.69 from the shopkeeper.

In a library, there are 700 books. Jane took 70 books and peter took 40 books. After few days, peter returned 23 books to the library. How many books are there in the library now?

Total number of books = 700 Number of books jane took = 70 Number of books peter took = 40 Number of books in the library = Total number of books – ( Number of books jane took + Number of books peter took) = 700 – (70 + 40) = 590 books After few days, Number of books peter returned = 23 Number of books in library = 590 + 23 = 613 books Therefore, the number of books in the library now = 613 books

A basketball team is getting ready for the next season. The team decided to practice for 3 hours on Mondays and Wednesdays and for 4 hours on Thursdays and Saturdays. How many hours will they be practicing every week?

Given Number of hours team practice on Mondays and Wednesdays = 3 + 3 = 6 hours Number of hours team practice on Thursdays and Saturdays = 4 + 4 = 8 hours Total number of hours team practice every week = 6 + 8 = 14 hours Therefore, the Number of hours team practice every week is 14 hours.

Rosy is the manager of a restaurant. 15 waiters are supposed to be at work. But 5 of them are sick. Rosy managed to call two more waiters to come in to the work. How many waiters are working today?

Given Number of waiters = 15 Number of sick waiters = 5 Number of additional waiters = 2 Number of waiters working today = (Number of waiters – Number of sick waiters) + Number of additional waiters = (15 – 5) + 2 = 12 waiters Therefore, the Number of waiters working today = 12 waiters.

Ram works at xyz company and his monthly salary is 30,000. His room rent is 7000 and other expenses are upto 2500. He will get an additional amount of 4500 from the bank as interest. How much money will be left with ram at the end of the month?

Given, Ram’s monthly salary = 30,000 Ram’s bank interest = 4500 His total monthly income = Monthly salary + bank interest = 30,000 + 4500 = 34,500 His monthly room rent = 7000 His other expenses = 2500 Ram’s Expenditure = Room rent + other expenses = 7000 + 2500 = 9500 Ram’s monthly savings = Income – Expenditure = 34,500 – 9500 = 25,000 Money left with ram at the end of the month = 25,000

Example 10:

The total sale of a shop in the month of may was Rs.8956321. If the sale for the first two weeks were Rs.2569865 and Rs.2175800, find the sale of the remaining weeks?

Given Sale of the first week = 2569865 Sale of the second week = 2175800 Sale in first two weeks = Sale in first week + Sale in the second week = 2569865 + 2175800 = 4745665 Total sale of the shop = 8956321 Sale in first two weeks = 4745665 Sale of remaining weeks = total sale of the shop – sale in first two weeks = 8956321 – 4745665 = 4210656 Therefore, the sale of the remaining weeks’ Rs. 4210656

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Mathematics 3 Quarter 1 – Module 16: Solving Problems Involving Subtraction

This module builds directly on your fluency with subtraction, addition, and mastery of reading with comprehension. This is the final module of the 1st Quarter. You are encouraged to apply the tools, representation, and concepts you have learned on problem-solving using subtraction and addition. The lesson requires you to demonstrate the flexibility of your thinking and reasoning for a variety of problem types. The lesson is arranged to follow the standard sequence of the course but the order in which you read them can be changed to correspond with the Grade 3 learning materials you are now using.

After going through this module, you are expected to:

1. Solve the routine problem in subtraction with addition including money using appropriate solving strategies.

Enjoy your journey. Good luck!

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Solving word problems both rely the development of reading and language skills. Addition means “putting together” groups of objects and finding how many they are in total while subtraction tells “how many are left” or “how many more or less”.

Steps in Problem Solving:

• Identify the Problem. Understand what is asked.
• Encircle important numbers.
• Underline the keywords. Analyze if it is for addition or subtraction .
• Solve the problem.
• Present the answer.

Addition: in all, sum, total, more than, plus, altogether, increased by add

Subtraction: fewer, left, less than, take away, minus, difference, remain, decreased

There are 6 surfboards and the surfer bought another 8 pieces. How many surfboards are there in all?

There were 8 beach balls but 5 of them were damaged. How many beach balls were left?

8 – 5 = 3

Solving Word Problems Involving Addition and Subtraction of Numbers within 120 Worksheets

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Visualizing and Solving One-Step Routine and Non-Routine Problems Involving Addition of Whole Numbers Including Money with Sums Up To 99 Using Appropriate Problem Solvi

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Visualizing and Solving One-Step Routine and Non-Routine Problems Involving Addition of Whole Numbers Including Money with Sums Up To 99 Using Appropriate Problem Solving Strategies

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