Subtract the ones, then the tens, then the hundreds. If a place is short, break one from the next place: a ten into 10 ones, or a hundred into 10 tens. You did this with tens in Subtracting Two-Digit Numbers.
Why it works
Breaking a hundred into 10 tens is a fair trade, just like breaking a ten into 10 ones. 5 hundreds and 3 tens is the same amount as 4 hundreds and 13 tens. But the hundred you broke is gone from the hundreds place, so that digit goes down by 1.
Worked example: Break twice
Find $532 - 175$.
- Ones: 2 is less than 5. Break a ten: 2 tens and 12 ones. $12 - 5 = 7$.
- Tens: 2 is less than 7. Break a hundred: 4 hundreds and 12 tens. $12 - 7 = 5$.
- Hundreds: $4 - 1 = 3$.
- Check: $357 + 175 = 532$.
Answer: $357$
Worked example: Zeros
Find $400 - 156$.
- There are no ones or tens to break, so break a hundred: 3 hundreds and 10 tens.
- Now break a ten: 9 tens and 10 ones.
- Ones: $10 - 6 = 4$. Tens: $9 - 5 = 4$. Hundreds: $3 - 1 = 2$.
Answer: $244$
Worked example: Count up instead
Find $400 - 156$ another way.
- 156 to 160 is 4.
- 160 to 200 is 40.
- 200 to 400 is 200.
- $4 + 40 + 200 = 244$.
Answer: $244$
Key idea
Subtract place by place. When a place is short, break a ten or a hundred, and lower the digit you broke it from. Add to check.
Common mistake
Breaking a hundred but forgetting to lower the hundreds digit, so $532 - 175$ comes out as 457. After the break there are only 4 hundreds. Check by adding: $457 + 175 = 632$, not 532.
Grown-up tip: Ask your child to cross out the digit they broke from and write the new digit above it.