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Long Multiplication with Decimals
(KS2, Year 5)

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Long multiplication is a method for multiplying numbers. Long multiplication can be used for numbers with digits after the decimal point. The long multiplication below shows what we mean by using a number with digits after the decimal point:

long multiplication with decimals In this long multiplication, 1.4 has a digit (4) after a decimal point (.).

A Real Example of How to Do Long Multiplication with Decimals

Doing long multiplication with decimals is easy.

Question

Multiply the numbers below. 25 times 1 point 4

Step-by-Step:

1

Write the numbers you wish to multiply, one underneath the other. 25 times 14 long multiplication decimals step 1
The trick with long multiplication with decimals is to ignore the decimal point at first and do a long multiplication as normal. 25 times 14 long multiplication decimals ignore decimal point

2

Find the right most digit of the bottom number (in the units column). 25 times 14 long multiplication decimals step 2

3

Find the right most digit of the top number (in the units column). 25 times 14 long multiplication decimals step 3

4

Multiply the bottom digit (4) with the top digit (5). 25 times 14 long multiplication decimals step 4
5 × 4 = 20

5

Check if the answer from Step 4 is 9 or less: No. 20 is not 9 or less.
  • If No, the answer will have two digits. 25 times 14 long multiplication decimals step 5 1
  • Write the digit on the right underneath the column (beneath the line). 25 times 14 long multiplication decimals step 5 2
  • Carry the left digit to the column to the left. 25 times 14 long multiplication decimals step 5 3

6

Move a digit to the left in the top number. 25 times 14 long multiplication decimals step 6

7

  • Multiply the bottom digit (4) with the top digit (2). 25 times 14 long multiplication decimals step 7 1
    2 × 4 = 8
  • Add any carried numbers to the answer. 25 times 14 long multiplication decimals step 7 2
    8 + 2 = 10

8

Check if the answer from Step 7 is 9 or less: No. 10 is not 9 or less.
  • If No, the answer will have two digits. 25 times 14 long multiplication decimals step 8 1
  • Write the digit on the right underneath the column (beneath the line). 25 times 14 long multiplication decimals step 8 2
  • Carry the left digit to the column to the left. 25 times 14 long multiplication decimals step 8 3

9

Move a digit to the left in the top number. 25 times 14 long multiplication decimals step 9 There are no more digits to the left.

10

Write the carried digit underneath the line. 25 times 14 long multiplication decimals step 10

11

Write a 0 on the right in a new row underneath the line.

25 times 14 long multiplication decimals step 11

12

Move a digit to the left in the bottom number (in the tens column). 25 times 14 long multiplication decimals step 12

13

Find the right most digit of the top number (in the units column). 25 times 14 long multiplication decimals step 13

14

Multiply the bottom digit (1) with the top digit (5). 25 times 14 long multiplication decimals step 14
5 × 1 = 5

15

Check if the answer from Step 4 is 9 or less: Yes. 5 is 9 or less.
  • If Yes, write the number beneath the line, to the left of the 0. 25 times 14 long multiplication decimals step 15

16

Move a digit to the left in the top number. 25 times 14 long multiplication decimals step 16

17

Multiply the bottom digit (1) with the top digit (2). 25 times 14 long multiplication decimals step 17
2 × 1 = 2

18

Check if the answer from Step 17 is 9 or less: Yes. 2 is 9 or less.
  • If Yes, write the number below beneath the line. 25 times 14 long multiplication decimals step 18

19

Move a digit to the left in the top number. 25 times 14 long multiplication decimals step 19 There are no more digits to the left.

20

Use long addition to add the two numbers beneath the line. 25 times 14 long multiplication decimals step 20
We have completed the long multiplication having ignored the decimal point. Now we consider the decimal point again.

21

Count the number of digits after the decimal point. 25 times 14 long multiplication decimals step 21 There is 1 digit after the decimal point (a 4).

22

Ensure there are as many digits after the decimal point (1) in the answer (350). 25 times 14 long multiplication decimals step 22 There is 1 digit after the decimal point (a 4).

Answer:

The solution to 25 × 1.4 is 35.

Lesson Slides

The slider below shows another real example of how to do long multiplication with decimals.

Parts of an Multiplication

product explained
  • The numbers you multiply together are factors.
  • The result of multiplying the numbers is the product.
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This page was written by Stephen Clarke.

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