Math Core

If a book has 543 pages and you have read 178, how many pages are left? To find out, you subtract. Subtracting three-digit numbers uses the same place value ideas as adding, just in reverse.

Subtract place by place

When each digit on top is at least as big as the digit below it, subtract one place at a time.

Worked example: No regrouping

Find $468 - 235$ .

Ones: $8 - 5 = 3$ .
Tens: $6 - 3 = 3$ .
Hundreds: $4 - 2 = 2$ .

The difference is 233.

When you need to regroup

What if the top digit is too small? In $543 - 178$ , you can't take 8 ones from 3 ones. So you regroup: trade 1 ten for 10 ones.

Worked example: Regrouping twice

Find $543 - 178$ .

\begin{array}{r} 543 \\ -\,178 \\ \hline 365 \end{array}

Ones: 3 is less than 8. Trade 1 of the 4 tens for 10 ones. Now there are 13 ones and 3 tens. $13 - 8 = 5$ .
Tens: 3 is less than 7. Trade 1 of the 5 hundreds for 10 tens. Now there are 13 tens and 4 hundreds. $13 - 7 = 6$ .
Hundreds: $4 - 1 = 3$ .

The difference is 365. The reader has 365 pages left.

Subtracting three-digit numbers

Line up the places. Start with the ones.
If the top digit is smaller than the bottom digit, trade 1 from the next place to the left for 10.
Subtract the ones, then the tens, then the hundreds.

Common mistake

Don't subtract the smaller digit from the bigger one just because it's easier. In $543 - 178$ , the ones digit is not $8 - 3 = 5$ . The top number must stay on top, so you regroup and find $13 - 8$ .

Subtracting across zeros

Numbers like 400 have zeros in the tens and ones. There is nothing to trade from the tens, so go to the hundreds first.

Worked example: Across zeros

Find $400 - 163$ .

400 is 4 hundreds. Trade 1 hundred for 10 tens: now it's 3 hundreds and 10 tens. Then trade 1 ten for 10 ones: 3 hundreds, 9 tens and 10 ones. That is still 400!

Ones: $10 - 3 = 7$ .
Tens: $9 - 6 = 3$ .
Hundreds: $3 - 1 = 2$ .

The difference is 237.

Counting up

You can also subtract by counting up from the smaller number. This works great when the numbers are close to a hundred.

Worked example: Count up to find the difference

Find $602 - 398$ .

Hop from 398 to 602 in friendly steps:

398 to 400 is 2.
400 to 600 is 200.
600 to 602 is 2.

Add the hops: $2 + 200 + 2 = 204$ . So $602 - 398 = 204$ .

Tip

Check subtraction with addition. If $543 - 178 = 365$ , then $365 + 178$ should give back 543. It does, so the answer is right.

Practice

Practice 1

Find $587 - 253$ .

Type a number.

Practice 2

Find $462 - 138$ .

Type a number.

Practice 3

Find $725 - 381$ .

Type a number.

Practice 4

Find $634 - 278$ .

Type a number.

Practice 5

Find $500 - 236$ .

Type a number.

Practice 6

A library had 612 books on its shelves. Kids checked out 275 of them. How many books are still on the shelves?

Type a number.

Practice 7

Find $803 - 457$ .

Type a number.

Practice 8

What number goes in the box? $\square + 348 = 715$

Type a number.