# 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:

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.

## Parts of an Multiplication

• The numbers you multiply together are factors.
• The result of multiplying the numbers is the product.

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