Addition and Subtraction with Regrouping
Grade 3 · Math · Study Guide
Learn how to add and subtract larger numbers by regrouping (carrying and borrowing).
Have you ever tried to add 47 + 35 and wondered what to do when the ones column adds up to more than 9? That's where regrouping comes in! Regrouping means you trade 10 ones for 1 ten, or 10 tens for 1 hundred — just like trading 10 pennies for a dime.
When you add 47 + 35, start in the ones column: 7 + 5 = 12. You can't write 12 in one column, so you write the 2 in the ones place and carry the 1 ten over to the tens column. Then 4 + 3 + 1 (carried) = 8 tens. Your answer is 82!
Subtraction with regrouping works the opposite way. If you try to subtract 52 − 27 and the top digit in the ones column is smaller than the bottom digit (2 is less than 7), you borrow 1 ten from the tens column. That turns the 2 into 12, and you now have enough to subtract. 12 − 7 = 5, and the tens become 4 − 2 = 2. Answer: 25.
Practice makes this automatic. The key is always starting in the ones place and working left. With regrouping, you can add and subtract any numbers — even ones in the hundreds!
| Step | What to Do | Example (47 + 35) |
|---|---|---|
| 1 | Add the ones column | 7 + 5 = 12 |
| 2 | Write the ones digit, carry the tens | Write 2, carry 1 |
| 3 | Add the tens column plus carried digit | 4 + 3 + 1 = 8 |
| 4 | Write the tens digit | Write 8 → Answer: 82 |
Key terms
- Regrouping
- Trading 10 of a smaller unit for 1 of the next larger unit (or vice versa) when adding or subtracting.
- Carry
- Moving a group of 10 to the next column to the left when adding.
- Borrow
- Taking 1 from the next column to the left when subtracting, turning it into 10 in the current column.
- Ones place
- The rightmost digit in a number — how many single units there are.
- Tens place
- The second digit from the right — how many groups of 10 there are.
Flashcards
- Regrouping in addition
- When the ones column sum is 10 or more, carry the extra ten to the tens column.
- Regrouping in subtraction
- When the top ones digit is smaller than the bottom, borrow 1 ten from the tens column.
- 47 + 35
- 94 (7+5=12, write 2 carry 1; 4+3+1=8)
- 83 − 46
- 37 (borrow to get 13−6=7; 7−4=3)
- Ones place
- The rightmost column in a number
- Tens place
- The second column from the right
Practice questions
What is 56 + 38?
- 84
- 94
- 88
- 74
Show answer
Answer: 94
6+8=14, write 4 carry 1; 5+3+1=9. So 56+38=94.
What is 73 − 45?
- 38
- 32
- 28
- 18
Show answer
Answer: 28
Borrow from tens: 13−5=8; 6−4=2. So 73−45=28.
When adding 64 + 57, you need to regroup in the ones column.
Show answer
Answer: True
4+7=11 in the ones column, which is more than 9, so regrouping is needed.
In the problem 82 − 47, you need to ___ from the tens place to subtract in the ones place.
Show answer
Answer: borrow
Since 2 < 7, you borrow 1 ten from the tens place, making the ones digit 12.
Sam had 124 stickers. He gave away 67. How many does he have left?
- 57
- 67
- 47
- 63
Show answer
Answer: 57
124−67: borrow to get 14−7=7; 1−6 requires borrow giving 11−6=5; 0 remaining. 124−67=57.
Fun facts
- The word 'regrouping' replaced 'borrowing' in math books because you never actually give anything back — you're just reorganizing!
- Ancient Egyptian mathematicians used regrouping over 4,000 years ago when they built the pyramids and needed to track huge numbers of stones.
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