In subtracting within 1,000 you broke a ten when you needed more ones. But what if there are no tens to break, as in $400 - 127$? Then you go one place further.
Why it works
$400$ can be shown as 3 hundreds, 9 tens and 10 ones, because $300 + 90 + 10 = 400$. Breaking one hundred into 10 tens, and then one of those tens into 10 ones, leaves 9 tens and 10 ones. Nothing is lost. The number just has enough in each place to subtract.
Key idea
When you need ones and the tens place is 0, break 1 hundred into 10 tens, then break 1 of those tens into 10 ones. A 0 in the tens becomes 9.
Worked example: From a hundred
Find $400 - 127$.
- Rewrite $400$ as 3 hundreds, 9 tens and 10 ones.
- Ones: $10 - 7 = 3$.
- Tens: $9 - 2 = 7$.
- Hundreds: $3 - 1 = 2$.
- Check: $273 + 127 = 400$.
Answer: $273$
Worked example: A zero in the middle
Find $503 - 268$.
- Ones: 3 is less than 8, and there are 0 tens. Break 1 hundred into 10 tens, then 1 ten into 10 ones: now 4 hundreds, 9 tens and 13 ones.
- Ones: $13 - 8 = 5$. Tens: $9 - 6 = 3$. Hundreds: $4 - 2 = 2$.
- Check: $235 + 268 = 503$.
Answer: $235$
Worked example: From a thousand
Find $1,000 - 365$.
- $1,000$ is 9 hundreds, 9 tens and 10 ones (break the thousand, then a hundred, then a ten).
- Ones: $10 - 5 = 5$. Tens: $9 - 6 = 3$. Hundreds: $9 - 3 = 6$.
Answer: $635$
Common mistake
Keeping 10 tens instead of 9. After breaking a hundred into 10 tens, one of those tens goes to the ones place. Only 9 tens are left. Using 10 tens gives $400 - 127 = 283$. The add-back check shows it: $283 + 127 = 410$, not $400$.
A shortcut for numbers like $400$: take 1 away from both numbers first. $400 - 127$ has the same answer as $399 - 126$, and that needs no regrouping at all: $273$.