Two partial products
326 x 14 means 326 x 4 and 326 x 10.
| Part | Value |
|---|---|
| 326 x 4 | 1,304 |
| 326 x 10 | 3,260 |
Add the partial products at the end.
Year 6
Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
Use long multiplication accurately when multiplying a 3- or 4-digit number by a 2-digit number.
Lesson overview
Number - addition, subtraction, multiplication and division
Long multiplication works by multiplying the number by each digit of the multiplier separately, starting with the ones and then the tens. The tens row is shifted one place to the left because it represents tens, not ones.
The tens row shifts left
The second row starts one place to the left because it stands for tens.
multiply by 4
multiply by 10
That place shift is part of the value, not decoration.
Worked example
Work out 326 x 14.
| Row | Product |
|---|---|
| 326 x 4 | 1,304 |
| 326 x 10 | 3,260 |
| Total | 4,564 |
- Multiply 326 by 4 to get 1,304.
- Multiply 326 by 10 to get 3,260.
- Add 1,304 and 3,260.
- So 326 x 14 = 4,564.
Try it
Keep each row aligned by place value before you add them.
Question 1
326 x 4 =
Question 2
326 x 10 =
Question 3
326 x 14 =
| Partial products |
|---|
| 1,304 and 3,260 |
Question 4
Which row in long multiplication must shift left one place?
4
10
Question 5
A sensible estimate for 326 x 14 is:
Common mistakes
Watch for these when working through the lesson.
- Forgetting that the tens row must shift left one place.
- Adding the partial products incorrectly at the end.
- Mixing up the order of multiplying by the ones and tens digits.
Related topics
These ideas fit closely with this lesson.
- Use long division carefully and interpret remainders.
- Use estimation to check answers to calculations.