Subtract Whole Numbers

Use Subtraction Notation

Suppose there are seven bananas in a bowl. Elana uses three of them to make a smoothie. How many bananas are left in the bowl? To answer the question, we subtract three from seven. When we subtract, we take one number away from another to find the difference. The notation we use to subtract $3$ from $7$ is

7 - 3

We read $7 - 3$ as seven minus three and the result is the difference of seven and three.

Subtraction Notation

To describe subtraction, we can use symbols and words.

Operation	Notation	Expression	Read as	Result
Subtraction	$-$	$7 - 3$	seven minus three	the difference of $7$ and $3$

Translate from math notation to words: ⓐ $8 - 1$ ⓑ $26 - 14$ .

Solution

ⓐ We read this as eight minus one. The result is the difference of eight and one.
ⓑ We read this as twenty-six minus fourteen. The result is the difference of twenty-six and fourteen.

Model Subtraction of Whole Numbers

A model can help us visualize the process of subtraction much as it did with addition. Again, we will use $base-10$ blocks. Remember a block represents 1 and a rod represents 10. Let’s start by modeling the subtraction expression we just considered, $7 - 3 .$

This table visually demonstrates the subtraction of 3 from 7 using blocks, illustrating each step from initial modeling to the final mathematical result.
We start by modeling the first number, 7.
Now take away the second number, 3. We'll circle 3 blocks to show that we are taking them away.
Count the number of blocks remaining.
There are 4 ones blocks left.	We have shown that $7 - 3 = 4$ .

Model the subtraction: $8 - 2 .$

Solution

$8 - 2$ means the difference of 8 and 2.
Model the first, 8.
Take away the second number, 2.
Count the number of blocks remaining.
There are 6 ones blocks left.	We have shown that $8 - 2 = 6$ .

Model the subtraction: $13 - 8 .$

Solution

Model the first number, 13. We use 1 ten and 3 ones.
Take away the second number, 8. However, there are not 8 ones, so we will exchange the 1 ten for 10 ones.
Now we can take away 8 ones.
Count the blocks remaining.
There are five ones left.	We have shown that $13 - 8 = 5$ .

As we did with addition, we can describe the models as ones blocks and tens rods, or we can simply say ones and tens.

Model the subtraction: $43 - 26 .$

Solution

Because $43 - 26$ means $43$ take away $26,$ we begin by modeling the $43 .$
An image containing two items. The first item is 4 horizontal rods containing 10 blocks each. The second item is 3 individual blocks.

Now, we need to take away $26,$ which is $2$ tens and $6$ ones. We cannot take away $6$ ones from $3$ ones. So, we exchange $1$ ten for $10$ ones.

Now we can take away $2$ tens and $6$ ones.
This image includes one row of base ten blocks at the top of the image; Next to it are seven individual blocks. Below this, is a group of two rows of base ten blocks, and two rows of 3 individual blocks with a circle around all. The arrow points to the right and shows one row of ten blocks and seven individual blocks underneath.

Count the number of blocks remaining. There is $1$ ten and $7$ ones, which is $17 .$

$43 - 26 = 17$

Addition and subtraction are inverse operations. Addition undoes subtraction, and subtraction undoes addition.

We know $7 - 3 = 4$ because $4 + 3 = 7 .$ Knowing all the addition number facts will help with subtraction. Then we can check subtraction by adding. In the examples above, our subtractions can be checked by addition.

\begin{matrix} 7 - 3 = 4 & because & 4 + 3 = 7 \\ 13 - 8 = 5 & because & 5 + 8 = 13 \\ 43 - 26 = 17 & because & 17 + 26 = 43 \end{matrix}

Subtract and then check by adding:

ⓐ $9 - 7$
ⓑ $8 - 3 .$

Solution

Illustration of subtracting 7 from 9, with expression, result, and addition-based verification.
ⓐ
	$9 - 7$
Subtract 7 from 9.	$2$
Check with addition. $2 + 7 = 9 ✓$

This table demonstrates the subtraction of 3 from 8, including the problem, its result, and a verification step.
ⓑ
	$8 - 3$
Subtract 3 from 8.	$5$
Check with addition. $5 + 3 = 8 ✓$

To subtract numbers with more than one digit, it is usually easier to write the numbers vertically in columns just as we did for addition. Align the digits by place value, and then subtract each column starting with the ones and then working to the left.

Subtract and then check by adding: $89 - 61 .$

Solution

This table illustrates the step-by-step process of subtracting two-digit numbers, including lining up, subtracting by place value, and checking with addition.
Write the numbers so the ones and tens digits line up vertically.	$\begin{matrix} 89 \\ \underset{____}{- 61} \end{matrix}$
Subtract the digits in each place value. Subtract the ones: $9 - 1 = 8$ Subtract the tens: $8 - 6 = 2$	$\begin{matrix} 89 \\ \underset{____}{- 61} \\ 28 \end{matrix}$
Check using addition. $\begin{matrix} 28 \\ \underset{____}{+ 61} \\ 89 \end{matrix}$

Our answer is correct.

When we modeled subtracting $26$ from $43,$ we exchanged $1$ ten for $10$ ones. When we do this without the model, we say we borrow $1$ from the tens place and add $10$ to the ones place.

Subtract: $43 - 26 .$

Solution

A step-by-step visual guide demonstrating the process of subtracting numbers with borrowing, including textual instructions and corresponding illustrations.
Write the numbers so each place value lines up vertically.
Subtract the ones. We cannot subtract 6 from 3, so we borrow 1 ten. This makes 3 tens and 13 ones. We write these numbers above each place and cross out the original digits.
Now we can subtract the ones. $13 - 6 = 7.$ We write the 7 in the ones place in the difference.
Now we subtract the tens. $3 - 2 = 1.$ We write the 1 in the tens place in the difference.
Check by adding. Our answer is correct.

Subtract and then check by adding: $207 - 64 .$

Solution

This table illustrates the step-by-step process of subtracting multi-digit numbers with borrowing, followed by a verification step.
Write the numbers so each place value lines up vertically.
Subtract the ones. $7 - 4 = 3.$ Write the 3 in the ones place in the difference.
Subtract the tens. We cannot subtract 6 from 0 so we borrow 1 hundred and add 10 tens to the 0 tens we had. This makes a total of 10 tens. We write 10 above the tens place and cross out the 0. Then we cross out the 2 in the hundreds place and write 1 above it.
Now we subtract the tens. $10 - 6 = 4.$ We write the 4 in the tens place in the difference.
Finally, subtract the hundreds. There is no digit in the hundreds place in the bottom number so we can imagine a 0 in that place. Since $1 - 0 = 1,$ we write 1 in the hundreds place in the difference.
Check by adding. Our answer is correct.

Subtract and then check by adding: $910 - 586 .$

Solution

Step-by-step guide demonstrating multi-digit subtraction with borrowing, showing instructional text alongside visual examples and a final check.
Write the numbers so each place value lines up vertically.
Subtract the ones. We cannot subtract 6 from 0, so we borrow 1 ten and add 10 ones to the 0 ones we had. This makes 10 ones. We write a 0 above the tens place and cross out the 1. We write the 10 above the ones place and cross out the 0. Now we can subtract the ones. $10 - 6 = 4.$
Write the 4 in the ones place of the difference.
Subtract the tens. We cannot subtract 8 from 0, so we borrow 1 hundred and add 10 tens to the 0 tens we had, which gives us 10 tens. Write 8 above the hundreds place and cross out the 9. Write 10 above the tens place.
Now we can subtract the tens. $10 - 8 = 2$ .
Subtract the hundreds place. $8 - 5 = 3$ Write the 3 in the hundreds place in the difference.
Check by adding. Our answer is correct.

Subtract and then check by adding: $2,162 - 479 .$

Solution

Write the numbers so each place value lines up vertically.
Subtract the ones. Since we cannot subtract 9 from 2, borrow 1 ten and add 10 ones to the 2 ones to make 12 ones. Write 5 above the tens place and cross out the 6. Write 12 above the ones place and cross out the 2.
Now we can subtract the ones.	$12 - 9 = 3$
Write 3 in the ones place in the difference.
Subtract the tens. Since we cannot subtract 7 from 5, borrow 1 hundred and add 10 tens to the 5 tens to make 15 tens. Write 0 above the hundreds place and cross out the 1. Write 15 above the tens place.
Now we can subtract the tens.	$15 - 7 = 8$
Write 8 in the tens place in the difference.
Now we can subtract the hundreds.
Write 6 in the hundreds place in the difference.
Subtract the thousands. There is no digit in the thousands place of the bottom number, so we imagine a 0. $1 - 0 = 1.$ Write 1 in the thousands place of the difference.
Check by adding. $\begin{matrix} \overset{1}{1}, \overset{1}{6} \overset{1}{8} 3 \\ \underset{______}{+ 479} \\ 2, 162 ✓ \end{matrix}$

Our answer is correct.

Translate Word Phrases to Math Notation

As with addition, word phrases can tell us to operate on two numbers using subtraction. To translate from a word phrase to math notation, we look for key words that indicate subtraction. Some of the words that indicate subtraction are listed in Table 12.

Operation	Word Phrase	Example	Expression
Subtraction	minus	$5$ minus $1$	$5 - 1$
	difference	the difference of $9$ and $4$	$9 - 4$
	decreased by	$7$ decreased by $3$	$7 - 3$
	less than	$5$ less than $8$	$8 - 5$
	subtracted from	$1$ subtracted from $6$	$6 - 1$

Translate and then simplify:

ⓐ the difference of $13$ and $8$
ⓑ subtract $24$ from $43$

Solution

ⓐ
The word difference tells us to subtract the two numbers. The numbers stay in the same order as in the phrase.

Steps to translate a verbal mathematical phrase into an expression and simplify it to its numerical value.

the difference of 13 and 8

Translate. $13 - 8$

Simplify. 5
ⓑ
The words subtract from tells us to take the first number away from the second. We must be careful to get the order correct.

This table illustrates the steps to translate a word problem into a mathematical expression and then simplify it to a numerical result.

subtract 24 from 43

Translate. $43 - 24$

Simplify. 19

Steps to translate a verbal mathematical phrase into an expression and simplify it to its numerical value.
	the difference of 13 and 8
Translate.	$13 - 8$
Simplify.	5

This table illustrates the steps to translate a word problem into a mathematical expression and then simplify it to a numerical result.
	subtract 24 from 43
Translate.	$43 - 24$
Simplify.	19

Subtract Whole Numbers in Applications

To solve applications with subtraction, we will use the same plan that we used with addition. First, we need to determine what we are asked to find. Then we write a phrase that gives the information to find it. We translate the phrase into math notation and then simplify to get the answer. Finally, we write a sentence to answer the question, using the appropriate units.

The temperature in Chicago one morning was $73$ degrees Fahrenheit. A cold front arrived and by noon the temperature was $27$ degrees Fahrenheit. What was the difference between the temperature in the morning and the temperature at noon?

Solution

We are asked to find the difference between the morning temperature and the noon temperature.

This table illustrates the step-by-step process of translating a word phrase into a subtraction problem and calculating its numerical difference.
Write a phrase.	the difference of 73 and 27
Translate to math notation. Difference tells us to subtract.	$73 - 27$
Then we do the subtraction.
Write a sentence to answer the question.	The difference in temperatures was 46 degrees Fahrenheit.

A washing machine is on sale for $$399 .$ Its regular price is $$588 .$ What is the difference between the regular price and the sale price?

Solution

We are asked to find the difference between the regular price and the sale price.

This table illustrates the step-by-step process of solving a subtraction word problem, from phrasing to the final answer.
Write a phrase.	the difference between 588 and 399
Translate to math notation.	$588 - 399$
Subtract.
Write a sentence to answer the question.	The difference between the regular price and the sale price is $189.

Key Concepts

Operation	Notation	Expression	Read as	Result
Subtraction	$-$	$7 - 3$	seven minus three	the difference of $7$ and $3$

Subtract whole numbers.
1. Write the numbers so each place value lines up vertically.
2. Subtract the digits in each place value. Work from right to left starting with the ones place. If the digit on top is less than the digit below, borrow as needed.
3. Continue subtracting each place value from right to left, borrowing if needed.
4. Check by adding.

Practice Makes Perfect

Use Subtraction Notation

In the following exercises, translate from math notation to words.

$15 - 9$

Solution

fifteen minus nine; the difference of fifteen and nine

$18 - 16$

$42 - 35$

Solution

forty-two minus thirty-five; the difference of forty-two and thirty-five

$83 - 64$

$675 - 350$

Solution

six hundred seventy-five minus three hundred fifty; the difference of six hundred seventy-five and three hundred fifty

$790 - 525$

Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.

$5 - 2$

Solution

The image uses blocks to demonstrate the subtraction problem 5 - 2.

$8 - 4$

$6 - 3$

Solution

The image uses blocks to demonstrate the subtraction problem 6- 3.

$7 - 5$

$18 - 5$

Solution

The image uses blocks to demonstrate the subtraction problem 18 - 5.

$19 - 8$

$17 - 8$

Solution

The image uses blocks to demonstrate the subtraction problem 17 - 8.

$17 - 9$

$35 - 13$

Solution

The image uses blocks to demonstrate the subtraction problem 35 - 13.

$32 - 11$

$61 - 47$

Solution

The image uses blocks to demonstrate the subtraction problem 61 - 47.

$55 - 36$

Subtract Whole Numbers

In the following exercises, subtract and then check by adding.

$9 - 4$

Solution

5

$9 - 3$

$8 - 0$

Solution

8

$2 - 0$

$38 - 16$

Solution

22

$45 - 21$

$85 - 52$

Solution

33

$99 - 47$

$493 - 370$

Solution

123

$268 - 106$

$5,946 - 4,625$

Solution

1,321

$7,775 - 3,251$

$75 - 47$

Solution

28

$63 - 59$

$461 - 239$

Solution

222

$486 - 257$

$525 - 179$

Solution

346

$542 - 288$

$6,318 - 2,799$

Solution

3,519

$8,153 - 3,978$

$2,150 - 964$

Solution

1,186

$4,245 - 899$

$43,650 - 8,982$

Solution

34,668

$35,162 - 7,885$

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate and simplify.

The difference of $10$ and $3$

Solution

10 − 3; 7

The difference of $12$ and $8$

The difference of $15$ and $4$

Solution

15 − 4; 11

The difference of $18$ and $7$

Subtract $6$ from $9$

Solution

9 − 6; 3

Subtract $8$ from $9$

Subtract $28$ from $75$

Solution

75 − 28; 47

Subtract $59$ from $81$

$45$ decreased by $20$

Solution

45 − 20; 25

$37$ decreased by $24$

$92$ decreased by $67$

Solution

92 − 67; 25

$75$ decreased by $49$

$12$ less than $16$

Solution

16 − 12; 4

$15$ less than $19$

$38$ less than $61$

Solution

61 − 38; 23

$47$ less than $62$

Mixed Practice

In the following exercises, simplify.

$76 - 47$

Solution

29

$91 - 53$

$256 - 184$

Solution

72

$305 - 262$

$719 + 341$

Solution

1,060

$647 + 528$

$2,015 - 1,993$

Solution

22

$2,020 - 1,984$

In the following exercises, translate and simplify.

Seventy-five more than thirty-five

Solution

75 + 35; 110

Sixty more than ninety-three

$13$ less than $41$

Solution

41 − 13; 28

$28$ less than $36$

The difference of $100$ and $76$

Solution

100 − 76; 24

The difference of $1,000$ and $945$

Subtract Whole Numbers in Applications

In the following exercises, solve.

Temperature The high temperature on June $2$ in Las Vegas was $80$ degrees and the low temperature was $63$ degrees. What was the difference between the high and low temperatures?

Solution

The difference between the high and low temperature was 17 degrees

Temperature The high temperature on June $1$ in Phoenix was $97$ degrees and the low was $73$ degrees. What was the difference between the high and low temperatures?

Class size Olivia’s third grade class has $35$ children. Last year, her second grade class had $22$ children. What is the difference between the number of children in Olivia’s third grade class and her second grade class?

Solution

The difference between the third grade and second grade was 13 children.

Class size There are $82$ students in the school band and $46$ in the school orchestra. What is the difference between the number of students in the band and the orchestra?

Shopping A mountain bike is on sale for $$399 .$ Its regular price is $$650 .$ What is the difference between the regular price and the sale price?

Solution

The difference between the regular price and sale price is $251.

Shopping A mattress set is on sale for $$755 .$ Its regular price is $$1,600 .$ What is the difference between the regular price and the sale price?

Savings John wants to buy a laptop that costs $$840 .$ He has $$685$ in his savings account. How much more does he need to save in order to buy the laptop?

Solution

John needs to save $155 more.

Banking Mason had $$1,125$ in his checking account. He spent $$892 .$ How much money does he have left?

Everyday Math

Road trip Noah was driving from Philadelphia to Cincinnati, a distance of $502$ miles. He drove $115$ miles, stopped for gas, and then drove another $230$ miles before lunch. How many more miles did he have to travel?

Solution

157 miles

Test Scores Sara needs $350$ points to pass her course. She scored $75, 50, 70, and 80$ on her first four tests. How many more points does Sara need to pass the course?

Writing Exercises

Explain how subtraction and addition are related.

Solution

Answers may vary.

How does knowing addition facts help you to subtract numbers?

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

A self-assessment table for subtraction skills, allowing students to rate their proficiency as 'Confidently', 'With some help', or 'No-I don't get it!' across five different learning objectives.

ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?