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Model the subtraction:
Because
means
take away
we begin by modeling the
Now, we need to take away
which is
tens and
ones. We cannot take away
ones from
ones. So, we exchange
ten for
ones.
Now we can take away
tens and
ones.
Count the number of blocks remaining. There is ten and ones, which is
Addition and subtraction are inverse operations. Addition undoes subtraction, and subtraction undoes addition.
We know because 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.
Subtract and then check by adding:
| ⓐ | |
| Subtract 7 from 9. | |
| Check with addition.
|
| ⓑ | |
| Subtract 3 from 8. | |
| Check with addition.
|
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:
| Write the numbers so the ones and tens digits line up vertically. | |
| Subtract the digits in each place value.
Subtract the ones: Subtract the tens: |
|
| Check using addition.
|
Our answer is correct.
Subtract and then check by adding:
86 − 54 = 32 because 54 + 32 = 86
Subtract and then check by adding:
99 − 74 = 25 because 74 + 25 = 99
When we modeled subtracting from we exchanged ten for ones. When we do this without the model, we say we borrow from the tens place and add to the ones place.
Subtract:
| 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. We write the 7 in the ones place in the difference. |
 |
| Now we subtract the tens. We write the 1 in the tens place in the difference. |
 |
Check by adding.
Our answer is correct. |
Subtract and then check by adding:
93 − 58 = 35 because 58 + 35 = 93
Subtract and then check by adding:
81 − 39 = 42 because 42 + 39 = 81
Subtract and then check by adding:
| Write the numbers so each place value lines up vertically. |
 |
| Subtract the ones.
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. We write the 4 in the tens place in the difference. |
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| 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 we write 1 in the hundreds place in the difference. |
 |
Check by adding.
Our answer is correct. |
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