In most class 3 classrooms there is a quiet moment every teacher recognises. A child who happily recites the table of 4 looks at 36 × 4 and stops. All the facts are in their head, but they can’t see how to put them together. That bridge is multiplication with regrouping, and once a child sees why it works, the fear usually disappears. In this guide from Educom, we explain it the way a teacher would at the board, with place value, worked examples, word problems and practice sums.
Short answer: Multiplication with regrouping is the method we use when multiplying the ones digits gives 10 or more. Write the ones digit of that product, carry the tens digit to the tens column, multiply the tens digit next, and add the carried number. For example, 36 × 4 = 144.
Key points at a glance
- Carrying and regrouping are two names for the same move.
- You regroup only when a digit-by-digit product reaches 10 or more.
- Multiply first, then add the carried number. Never the other way round.
- A quick estimate tells you whether your answer is sensible.
This lesson sits inside our larger guide to multiplication for class 3.
What does regrouping mean in multiplication?
Regrouping means exchanging ones for tens when a place holds too many. Each place value column can hold only one digit, so when a product has two digits, the extra tens move to the next column.
Take 6 × 4 = 24. That is 24 ones, which is the same as 2 tens and 4 ones. We write the 4 in the ones place and carry the 2 tens across. Teachers also say “carry over”, and in the multiplication of 2-digit by 1-digit numbers the idea never changes.
A few terms help here. The 2-digit number is the multiplicand, the 1-digit number is the multiplier, and the answer is the product.
What should a child know before starting?
Two things make this topic much smoother.
- Tables from 2 to 10. Most wrong answers come from a shaky table fact, not from the method.
- Place value. In 36, the 3 stands for 3 tens (30) and the 6 stands for 6 ones.
If either feels wobbly, spend a week there first. It saves a lot of frustration later.
Start with a sum that needs no regrouping
23 × 3
- Ones: 3 × 3 = 9
- Tens: 2 × 3 = 6 tens, which is 60
- Answer: 60 + 9 = 69
The ones product (9) is a single digit, so nothing moves. Regrouping begins only when that product reaches 10 or more.
Step-by-step method for multiplication with regrouping
- Write the 2-digit number on top and the 1-digit number below it, with ones under ones.
- Multiply the ones digit by the bottom number.
- If the product is 10 or more, write its ones digit and carry its tens digit above the tens column.
- Multiply the tens digit by the bottom number.
- Add the carried number to that result.
- Write the total to the left of the ones digit you already wrote.
Example 1, 36 × 4
2
3 6
× 4
—–
1 4 4
- Ones: 6 × 4 = 24. Write 4, carry 2.
- Tens: 3 × 4 = 12, and 12 + 2 = 14.
- Write 14 to the left of the 4. 36 × 4 = 144
Example 2, 47 × 5
- Ones: 7 × 5 = 35. Write 5, carry 3.
- Tens: 4 × 5 = 20, and 20 + 3 = 23.
- 47 × 5 = 235
Example 3, 58 × 6
- Ones: 8 × 6 = 48. Write 8, carry 4.
- Tens: 5 × 6 = 30, and 30 + 4 = 34.
- 58 × 6 = 348
Quick reference table
| Sum | Ones product | Carry | Tens product plus carry | Answer |
| 27 × 3 | 21 | 2 | 6 + 2 = 8 | 81 |
| 45 × 6 | 30 | 3 | 24 + 3 = 27 | 270 |
| 68 × 4 | 32 | 3 | 24 + 3 = 27 | 272 |
| 84 × 7 | 28 | 2 | 56 + 2 = 58 | 588 |
Why does carrying work? Seeing it through place value
Children remember a method far better when they know the reason behind it. Break 36 into 30 and 6, the expanded form, and multiply each part by 4.
| Multiply | 30 | 6 |
| 4 | 120 | 24 |
Add the two partial products: 120 + 24 = 144.
It is the same answer as before. When we “carry the 2”, we are simply adding the 2 tens hidden inside 24 to the tens from 3 × 4. The vertical layout is a shorter way to write what the box shows in full. Many teachers show this area model first, then move to the shorter form once the idea has settled.
For a hands-on version, bundle ice-cream sticks into tens. Make 4 groups of 36 sticks, then watch the loose sticks pile up to 24 and swap 20 of them for 2 new bundles. Children rarely forget what they have physically done.
How can a child check the answer?
- Estimate. Round 36 to 40. Since 40 × 4 = 160, an answer near 160 (like 144) is believable, and an answer like 1,244 is not.
- Use expanded form. Multiply tens and ones separately, then add.
- Use repeated addition. 36 + 36 + 36 + 36 should also give 144.
Word problems on two digit multiplication with regrouping
Problem 1. A bus carries 45 children. How many children travel in 3 such buses?
45 × 3. Ones: 5 × 3 = 15, write 5, carry 1. Tens: 4 × 3 = 12, and 12 + 1 = 13. Answer: 135 children.
Problem 2. A sweet shop packs 28 laddoos in each box. How many laddoos are in 6 boxes?
28 × 6. Ones: 8 × 6 = 48, write 8, carry 4. Tens: 2 × 6 = 12, and 12 + 4 = 16. Answer: 168 laddoos.
Problem 3. One pen costs ₹18. What is the cost of 7 pens?
18 × 7. Ones: 8 × 7 = 56, write 6, carry 5. Tens: 1 × 7 = 7, and 7 + 5 = 12. Answer: ₹126.
Words like “each”, “every” and “in all” usually point towards multiplication.
Practice sums with answers
- 24 × 4
- 37 × 3
- 48 × 2
- 56 × 5
- 63 × 7
- 74 × 6
- 85 × 4
- 29 × 8
- 91 × 9
- A sheet has 45 stickers. How many stickers are there on 7 sheets?
Answers: 1) 96 2) 111 3) 96 4) 280 5) 441 6) 444 7) 340 8) 232 9) 819 10) 315
Sum 9 is a good one to discuss. The ones product is 9, so nothing is carried from the ones place, but the tens product (81) still produces a three-digit answer.
Common mistakes and how to fix them
| What goes wrong | Example | The fix |
| Forgetting the carry | 36 × 4 = 124 | Write the carry small, in a different colour, and tick it off after adding |
| Adding the carry too early | (3 + 2) × 4 = 20 | Always multiply the tens first, then add |
| Writing both digits of the product in one place | 24 written under the ones | Only the ones digit stays. The tens digit travels |
| Misaligned digits | Tens written under ones | Use squared notebooks |
| Guessing table facts | 7 × 8 = 54 | Revise tables daily for a few minutes |
Most of these are habit problems rather than understanding problems, so a little regular practice fixes them quickly.
Tips for parents and teachers
- Go from concrete to pictorial to abstract. Start with sticks or beads, move to drawings or the area box, and only then use the shorter vertical layout.
- Keep sessions short. Five or six sums a day beat a long weekend marathon.
- Ask your child to explain it back. If they can teach the steps to a younger sibling, they understand them.
- Praise the thinking. “I like how you checked with an estimate” builds more confidence than “correct”.
- Introduce multiplication with regrouping only after no-carry sums feel easy. Rushing the order is the most common reason children lose confidence.
When to ask for extra help
If your child keeps making the same errors after a few weeks of steady practice, a gap may be hiding further back, in tables, place value or addition with carrying. A good tutor can find it in a single session. Educom’s online maths classes for class 3 to 10 are built around exactly this kind of step-by-step explanation.
Multiplication with regrouping is less about memorising a trick and more about understanding place value. Multiply the ones, carry the extra tens, multiply the tens, add the carry, and check with a quick estimate. With short, regular practice, most children handle it comfortably.
Frequently asked questions
1. What is regrouping in multiplication?
Regrouping is exchanging ones for tens when a product has two digits. If 6 × 4 gives 24, we keep 4 ones and move 2 tens to the next column.
2. Is carrying the same as regrouping?
Yes. Carrying is the everyday word and regrouping is the mathematical term. Both describe moving extra tens to the next place value.
3. When do we regroup in multiplication?
Only when the product of two digits is 10 or more. If the product is 9 or less, the digit is written directly and nothing is carried.
4. Which class learns 2-digit by 1-digit multiplication?
Most Indian schools introduce it in class 3 or class 4, depending on the board and school. In the US, similar content usually appears in grade 3 or grade 4.
5. Why does my child forget to add the carry?
Usually because the carried digit is easy to lose track of. Writing it small above the tens column, in a different colour, and ticking it once added helps a lot.
6. What is the area model for multiplication?
It is a box that splits a number into tens and ones. For 36 × 4, the box shows 30 × 4 = 120 and 6 × 4 = 24, and the total is 144. It shows why regrouping works.
7. Is there a quick mental maths trick for multiplying by 5?
Yes. Multiply by 10 and halve the result. For 47 × 5, 47 × 10 = 470, and half of 470 is 235.
8. Can we multiply the tens first instead of the ones?
Yes. This is the partial products method, where you multiply tens and ones separately and then add. The standard method starts from the ones because carrying then flows naturally to the left.
9. How many sums should a child practise each day?
Five to ten sums, for about 10 to 15 minutes, is plenty. Consistency matters more than volume.
10. How can I check my answer without a calculator?
Round the 2-digit number to the nearest ten and multiply. If your answer is close to that estimate, it is probably right.