How to explain borrowing in subtraction (regrouping), step by step

Quick answer

Borrowing, now called regrouping, means trading 1 ten for 10 ones when the top digit is too small. In 52 − 27 you can't take 7 from 2, so trade a ten: 52 becomes 4 tens and 12 ones. Then 12 − 7 = 5 and 4 − 2 = 2, giving 25. Kids learn it in 2nd grade and are fluent within 1,000 by the end of 3rd grade.

“You can't take 7 from 2, so borrow from the 5” is how many of us learned it, usually without knowing why. Kids who understand the why make fewer mistakes, especially with zeros. Here is borrowing explained as a simple trade, first with blocks, then on paper.

Borrowing or regrouping? What the words mean

Schools today mostly say regrouping, and it's the more accurate word. Nothing is borrowed and nothing is paid back. You just trade 1 ten for 10 ones (or 1 hundred for 10 tens). The number keeps its value, it's only packed differently: 52 is 5 tens and 2 ones, and it is also 4 tens and 12 ones.

It's like breaking a dollar into dimes: same money, smaller pieces. Use the word your child's teacher uses, and mention the other so homework instructions never confuse them.

When kids learn it

These are the Common Core standards, used by most states; yours may differ. Before starting, check that your child knows 52 means 5 tens and 2 ones and can do teen facts like 12 − 7 without long counting. If not, our guide on how to teach subtraction covers those earlier steps.

How to teach subtraction with regrouping, step by step

Use base-ten blocks or bundles of 10 straws with rubber bands, plus a paper place-value mat labeled Tens and Ones. We'll solve 52 − 27.

Step 1: Build only the top number

Unlike addition, you build only the first number: 5 tens and 2 ones. The 27 isn't a pile of blocks; it is the amount you will take away.

Step 2: Check the ones: are there enough?

Always start with the ones. We need to take away 7 ones, but there are only 2. Ask, “Do we have enough ones?” No, so we need more ones.

Step 3: Trade 1 ten for 10 ones

Take one ten, slip off the rubber band (or swap the rod for 10 cubes), and put the 10 ones in the Ones column. Now there are 4 tens and 12 ones. Count to check it's still 52.

Step 4: Subtract the ones, then the tens

Take away 7 ones: 12 − 7 = 5. Take away 2 tens: 4 − 2 = 2. What's left is 2 tens and 5 ones: 25.

Step 5: Write it in columns and check by adding

Now record the same moves. Cross out the 5 and write 4 above it (the tens you have left), write 12 above the ones, then subtract each column.

41252−2725

Finish every problem by checking with addition: 25 + 27 = 52. If the check doesn't work, look for the column where something went wrong.

A 3-digit example: 645 − 278

Three-digit subtraction uses the same trade, sometimes twice.

1. Ones: 5 − 8 won't work. Trade 1 ten: 4 tens become 3 tens, and 5 ones become 15. 15 − 8 = 7.
2. Tens: 3 − 7 won't work. Trade 1 hundred: 6 hundreds become 5, and 3 tens become 13. 13 − 7 = 6.
3. Hundreds: 5 − 2 = 3.

51315645−278367

Check: 367 + 278 = 645. ✓

Borrowing across zero

Zeros are where many kids get stuck. In 403 − 127, the ones need a ten, but the tens place is empty. So go one more place over:

1. Trade 1 hundred for 10 tens: 3 hundreds, 10 tens, 3 ones.
2. Trade 1 of those tens for 10 ones: 3 hundreds, 9 tens, 13 ones.
3. Subtract: 13 − 7 = 6, 9 − 2 = 7, 3 − 1 = 2. The answer is 276.

3913403−127276

A neat shortcut: read 403 as 40 tens and 3 ones. Take 1 ten and you have 39 tens and 13 ones, done in one step. The same works for 500 − 248: 50 tens become 49 tens, and the 0 ones become 10. Then 10 − 8 = 2, 9 − 4 = 5, 4 − 2 = 2, so the answer is 252.

4910500−248252

Another trick: subtract 1 from both numbers. 499 − 247 has the same answer, 252, and needs no regrouping at all. Check by adding: 252 + 248 = 500.

Other ways to subtract

The column method isn't the only correct way, and mental strategies are great for checking.

• Counting up. For 52 − 27, count up from 27: 3 more to 30, 20 more to 50, 2 more to 52. 3 + 20 + 2 = 25.
• Compensation. For 52 − 29, subtract 30 instead (an easy jump) to get 22. You took away 1 too many, so add it back: 23.

Common mistakes (and how to fix them)

• The smaller-from-larger bug. In 52 − 27, the child does 7 − 2 = 5 in the ones and writes 35. Remind them the top number is what you start with, and ask “Are there enough ones on top?”
• Trading without crossing out. The child turns 2 into 12 but leaves the 5 tens as 5, again getting 35. Insist on crossing out and writing the new digit every time.
• Regrouping when it isn't needed. In 58 − 23, 8 is bigger than 3, so no trade is needed. Mix these problems in and ask first.
• Getting stuck at a zero. Remind them that an empty place means “go next door,” or use the 40-tens shortcut.
• Misaligned columns. In 345 − 62, the 6 must sit under the 4, not the 3. Grid paper helps.

Games and everyday practice

• Race to zero. Each player starts with 10 tens (100). Take turns rolling two dice and removing that many ones, trading a ten for 10 ones whenever you run out. First to reach zero wins.
• Making change. “This costs 65¢ and you pay with a dollar. How much change?” Count up with real coins: 5¢ to 70¢, then 30¢ more to a dollar, so 35¢.
• Pages left. “You've read 87 pages of a 112-page book. How many are left?”

Practice problems

Most of these need regrouping, but not all. Check each answer by adding.

Subtraction with regrouping (with answers)

1. 52 − 27 = ?
2. 61 − 34 = ?
3. 80 − 46 = ?
4. 73 − 29 = ?
5. 58 − 23 = ?
6. 90 − 57 = ?
7. 342 − 118 = ?
8. 645 − 278 = ?
9. 403 − 127 = ?
10. 500 − 248 = ?
11. 805 − 309 = ?
12. 700 − 365 = ?

Show answers

Print more from our free subtraction worksheets. If carrying in addition still needs work, start with our addition with regrouping guide; it's the same trade in reverse. To see where this fits in the school year, visit our 2nd grade and 3rd grade skills pages.

Frequently asked questions

How do you explain borrowing in subtraction to a child?

Explain it as a trade. If there aren't enough ones to take away, open up one ten and turn it into 10 ones. In 52 − 27, the 52 becomes 4 tens and 12 ones. It is still 52, just packed differently. Now there are enough ones: 12 − 7 = 5, then 4 − 2 = 2 tens, so the answer is 25.

Why do teachers say regrouping instead of borrowing?

“Borrowing” suggests you take something and give it back later, which never happens in subtraction. “Regrouping” describes what really happens: a ten is regrouped as 10 ones (or a hundred as 10 tens), and the number's value stays the same. Both words describe the same written steps, so it is fine to use both at home.

How do you borrow from zero in subtraction?

When the next place is 0, go one more place to the left. In 403 − 127, trade 1 hundred for 10 tens, then 1 of those tens for 10 ones: 403 becomes 3 hundreds, 9 tens and 13 ones. A shortcut is to read 403 as 40 tens and 3 ones, take 1 ten, and write 39 tens and 13 ones. The answer is 276.

What grade learns subtraction with regrouping?

In the Common Core standards, 2nd graders subtract fluently within 100 (2.NBT.B.5) and within 1,000 using models, including decomposing tens and hundreds (2.NBT.B.7). 3rd graders are fluent within 1,000 (3.NBT.A.2), and the standard written algorithm is required in 4th grade (4.NBT.B.4), though many schools teach it earlier.

How do you check a subtraction answer?

Add the answer to the number you subtracted. If you get the top number, the subtraction is right: for 52 − 27 = 25, check 25 + 27 = 52. This habit catches most regrouping slips and reminds children that addition and subtraction undo each other.

Why does my child subtract the smaller number from the bigger one?

In a problem like 52 − 27, a child may look at the ones column, see 2 and 7, and do 7 − 2 because it feels possible. That gives 35 instead of 25. Remind them that the top number is the one you start with, and ask “Are there enough ones on top?” before each column.

Sources

• Common Core State Standards: Grade 2, Number & Operations in Base Ten — CCSSI
• Common Core State Standards: Grade 3, Number & Operations in Base Ten — CCSSI
• Common Core State Standards: Grade 4, Number & Operations in Base Ten — CCSSI

Written by The Mathing Team for parents and teachers. Grade expectations follow the Common Core State Standards for Mathematics; your state or school may sequence skills a little differently.