Subtraction with borrowing across zeros, explained for parents

Schools usually call it regrouping or trading. You need it when the bottom digit in a column is bigger than the top digit, so you cannot take it away.

Take 52 − 27. In the ones, 2 − 7 does not work with whole numbers. So we take one ten from the 5 tens. That leaves 4 tens, and the ones become 12. Now 12 − 7 = 5 and 4 − 2 = 2. The answer is 25.

It is the opposite of carrying in addition. When you add, ten ones become one ten and move left. When you subtract, one ten breaks into ten ones and moves right. If carrying is still new, our post on teaching carrying is a good place to start.

Look at 503 − 267. The ones column needs to borrow: 3 − 7 will not work. So your child looks next door to the tens. There is nothing there. Zero tens. You cannot take a ten from nothing.

This is where kids invent rules. Some write 7 − 3 instead. Some skip the zero and take from the 5 but forget to change the zero at all. Both give wrong answers that look reasonable.

The fix is to read 503 differently. It is not “5, 0, 3.” It is 50 tens and 3 ones. If you can see the 50 tens, you can take one of them.

1. 1Start with the ones: 3 − 7 needs a borrow.
2. 2The tens digit is 0, so go one more column left to the hundreds. Take one hundred: the 5 becomes 4.
3. 3That hundred becomes ten tens, so the 0 in the tens becomes 10.
4. 4Now take one of those tens for the ones: the 10 becomes 9, and the 3 ones become 13.
5. 5Subtract each column from the right: 13 − 7 = 6, then 9 − 6 = 3, then 4 − 2 = 2.
6. 6The answer is 236.

Many teachers show a shortcut for step 2 and 3 together: cross out the 50 and write 49 above it. Fifty tens, take one away, forty-nine tens. That is the same thing in one move, and some kids find it much easier.

The same idea stretches as far as it needs to. In 4002 − 1357, the ones need to borrow, and the tens and hundreds are both zero.

Read the top number as 400 tens and 2 ones. Take one ten: 399 tens are left, and the ones become 12. On paper that means the 4 becomes 3, each zero becomes 9, and the 2 becomes 12.

Then subtract right to left: 12 − 7 = 5, then 9 − 5 = 4, then 9 − 3 = 6, then 3 − 1 = 2. The answer is 2645.

A quick check: 2645 + 1357 = 4002. Right again.

• Subtracting the smaller digit from the bigger one in every column. For 503 − 267 this gives 364. Ask, “Are we taking 3 from 7, or 7 from 3?” The top number is always the one we start with.
• Changing the zero to 10 and stopping there. The 10 then has to give one to the ones column, so it ends up as 9. If you see a 10 left over in the work, this is what happened.
• Forgetting to reduce the digit they borrowed from. The answer comes out a hundred (or a ten) too big.
• Borrowing when they do not need to. Before each column, ask: is the top digit big enough? If it is, no borrowing.

When you spot one of these, resist fixing it for them. Point at the column and ask what the digits are worth. If you want a script for that, our post on checking homework without doing it has a few.

Build up in small steps, one or two problems at each level:

1. 1No zeros, one borrow: 82 − 49.
2. 2A zero in the ones of the top number: 70 − 26.
3. 3A zero in the tens: 604 − 238.
4. 4Two zeros: 300 − 147.
5. 5Two zeros in a four-digit number: 5003 − 2468.

Ask for an estimate before each one. 300 − 147 is about 300 − 150, so the answer should be around 150. If they get 253, the estimate tells them to look again.

The subtraction with borrowing practice page has a one-page summary of the steps and the common mistakes, if you want something to keep next to the homework.

On the pad, the borrow boxes sit above the top number, so your child writes the new digits (the 4, the 9, the 13) right where they would on paper. MathPad checks each one, and if a digit is off it explains that step instead of giving the answer away.