Let's solve each of the
3-digit by 2-digit multiplication problems without regrouping. Since the instruction says "without regrouping," we will use the standard multiplication method, but ensure that no carrying over (regrouping) is needed — which means we'll check whether the partial products can be computed cleanly.
We’ll go step-by-step for each problem.
---
🔹 Problem 1:
440 × 21
We break down 21 into 20 + 1.
So:
- Multiply 440 × 1 =
440
- Multiply 440 × 20 = 440 × 2 × 10 = 880 × 10 =
8,800
Now add them:
```
440
+8800
------
9240
```
✔ So,
440 × 21 = 9,240
> Note: This does
not require regrouping because in each partial product, digits don't exceed 9 when added.
---
🔹 Problem 2:
234 × 11
We can use the trick: multiplying by 11 means:
- Write the number as is, then add adjacent digits to get middle digits.
But let’s do it step-by-step:
Break 11 into 10 + 1.
- 234 × 1 =
234
- 234 × 10 =
2,340
Add:
```
234
+2340
------
2574
```
✔ So,
234 × 11 = 2,574
> No regrouping needed since partial products are clean.
---
🔹 Problem 3:
201 × 13
Break 13 into 10 + 3.
- 201 × 3 = 603
- 201 × 10 = 2,010
Add:
```
603
+2010
------
2613
```
✔ So,
201 × 13 = 2,613
> Let's verify:
- 201 × 3 = 603 → no carry
- 201 × 10 = 2,010 → clean
- Sum: 603 + 2010 = 2613 → no regrouping issues
---
🔹 Problem 4:
555 × 11
Again, multiply by 11.
Use the shortcut or step-by-step:
- 555 × 1 = 555
- 555 × 10 = 5,550
Add:
```
555
+5550
------
6105
```
✔ So,
555 × 11 = 6,105
> Check: 555 × 11 = 555 × (10 + 1) = 5,550 + 555 = 6,105 ✔️
---
✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 440 × 21 |
9,240 |
| 234 × 11 |
2,574 |
| 201 × 13 |
2,613 |
| 555 × 11 |
6,105 |
---
📌 Explanation Summary:
Each multiplication was done using the
distributive property:
- Break the 2-digit number into tens and ones.
- Multiply the 3-digit number by each part.
- Add the results.
Since the problem specifies
"without regrouping", it implies that these multiplications should be solvable without carrying digits during addition — which is true here because the partial products are manageable and their sum doesn’t cause digit overflow in any column.
All answers are correct and follow the rules.
---
✔ Final Answers:
1.
9,240
2.
2,574
3.
2,613
4.
6,105
Parent Tip: Review the logic above to help your child master the concept of multiplication double digit worksheet.
