Properties of Subtraction
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.
Subtraction of 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.
\(\begin{array}{ccccccc}\phantom{\rule{1em}{0ex}}7-3=4\hfill & & & \text{because}\hfill & & & \phantom{\rule{1em}{0ex}}4+3=7\hfill \\ \phantom{\rule{0.5em}{0ex}}13-8=5\hfill & & & \text{because}\hfill & & & \phantom{\rule{1em}{0ex}}5+8=13\hfill \\ 43-26=17\hfill & & & \text{because}\hfill & & & 17+26=43\hfill \end{array}\)
Example
Subtract and then check by adding:
- \(9-7\)
- \(8-3.\)
Solution
| (a) | |
| \(9-7\) | |
| Subtract 7 from 9. | \(2\) |
| Check with addition. \(2+7=9✓\) |
| (b) | |
| \(8-3\) | |
| Subtract 3 from 8. | \(5\) |
| Check with addition. \(5+3=8✓\) |
Extra:
Subtract and then check by adding:
\(7-0\)
Solution:
7 − 0 = 7; 7 + 0 = 7
Extra:
Subtract and then check by adding:
\(6-2\)
Solution
6 − 2 = 4; 2 + 4 = 6
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.
Example
Subtract and then check by adding: \(89-61.\)
Solution
| Write the numbers so the ones and tens digits line up vertically. | \(\begin{array}{r} 89 \\ \underline{-\;61} \\ \end{array}\) |
| Subtract the digits in each place value. Subtract the ones: \(9-1=8\) Subtract the tens: \(8-6=2\) |
\(\begin{array}{r} 89 \\ -\;61 \\ \hline 28 \\ \end{array}\) |
|
Check using addition. |
Our answer is correct.
Extra:
Subtract and then check by adding: \(86-54.\)
Solution
86 − 54 = 32 because 54 + 32 = 86
Extra:
Subtract and then check by adding: \(99-74.\)
Solution
99 − 74 = 25 because 74 + 25 = 99
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.
This lesson is part of:
Introducing Numbers