Subtracting Whole Numbers

Learning Outcomes

Subtract single-digit numbers and check the solution using addition
Use columns representing place value to subtract multiple-digit numbers

Subtract Whole Numbers

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.

$7-3=4$	because	$4+3=7$
$13-8=5$	because	$5+8=13$
$43-26=17$	because	$17+26=43$

Exercise

Subtract and then check by adding:

$9 - 7$
$8 - 3$ .

Solution

1.
$9 - 7$
Subtract 7 from 9.	$2$
Check with addition. $2+7=9\quad\checkmark$

2.
$8 - 3$
Subtract 3 from 8.	$5$
Check with addition. $5+3=8\quad\checkmark$

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.

Exercise

Subtract and then check by adding:

89 - 61

Answer: Solution

Write the numbers so the ones and tens digits line up vertically.	$\begin{array}{c}\hfill 89\\ \hfill \underset{\text{____}}{-61}\end{array}$
Subtract the digits in each place value. Subtract the ones: $9 - 1=8$ Subtract the tens: $8 - 6=2$	$\begin{array}{c}\hfill 89\\ \hfill \underset{\text{____}}{-61}\\ \hfill 28\end{array}$
Check using addition. $\begin{array}{c}\hfill 28\\ \hfill \underset{\text{____}}{+61}\\ \hfill 89\end{array}\quad\checkmark$

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.

Find the difference of whole numbers

Write the numbers so each place value lines up vertically.
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.
Continue subtracting each place value from right to left, borrowing if needed.
Check by adding.

excercise

Subtract:

43 - 26

Answer: Solution

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.

Exercise

Subtract and then check by adding:

207 - 64

Answer: Solution

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. 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.

try it

Subtract and then check by adding:

439 - 52

Answer: $439 − 52 = 387$ because $387 + 52 = 439\quad\checkmark$

Subtract and then check by adding:

318 - 75

Answer: $318 − 75 = 243$ because $243 + 75 = 318\quad\checkmark$

Exercise

Subtract and then check by adding:

910 - 586

Answer: Solution

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 $10$ 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.

Exercise

Subtract and then check by adding:

2,162 - 479

Answer: Solution

Write the numbers so each place values line 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. $\begin{array}{}\\ \stackrel{1}{1},\stackrel{1}{6}\stackrel{1}{8}3\hfill \\ \underset{\text{______}}{+479}\hfill \\ 2,162\quad\checkmark \hfill \end{array}\quad\checkmark$