# Long Multiplication with Decimals(KS2, Year 5)

## The Lesson

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: 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. # 1

Write the numbers you wish to multiply, one underneath the other. The trick with long multiplication with decimals is to ignore the decimal point at first and do a long multiplication as normal. # 2

Find the right most digit of the bottom number (in the units column). # 3

Find the right most digit of the top number (in the units column). # 4

Multiply the bottom digit (4) with the top digit (5). 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. • Write the digit on the right underneath the column (beneath the line). • Carry the left digit to the column to the left. # 6

Move a digit to the left in the top number. # 7

• Multiply the bottom digit (4) with the top digit (2). 2 × 4 = 8 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. • Write the digit on the right underneath the column (beneath the line). • Carry the left digit to the column to the left. # 9

Move a digit to the left in the top number. There are no more digits to the left.

# 10

Write the carried digit underneath the line. # 11

Write a 0 on the right in a new row underneath the line. # 12

Move a digit to the left in the bottom number (in the tens column). # 13

Find the right most digit of the top number (in the units column). # 14

Multiply the bottom digit (1) with the top digit (5). 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. # 16

Move a digit to the left in the top number. # 17

Multiply the bottom digit (1) with the top digit (2). 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. # 19

Move a digit to the left in the top number. There are no more digits to the left.

# 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. 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). There is 1 digit after the decimal point (a 4).

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. Open the slider in a new tab

## Parts of an Multiplication • The numbers you multiply together are factors.
• The result of multiplying the numbers is the product.
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