# Calculating with decimals

**Adding and subtracting decimals**

When adding or subtracting decimals, the decimal points should be lined up.

**Short multiplication**

Short multiplication of decimals requires two steps:

Multiply 3.36 x 6

Start with the non decimal sections (this is to provide an estimate):

3.36 x 6 or 3 x 6 = 18

Then work on the decimals:

3.36 x 6 is equivalent to 336 x 6 ÷ 100

Answer is 20.16

**Long multiplication**

Long multiplication requires the following steps:

Multiply 58.5 x 35

Start with the non decimal sections (this is to provide an estimate):

58.5 x 35 or 58 x 35 = 2,030

Then work on the decimals:

58.5 x 10 x 35 ÷ 10

=585 x 35 ÷ 10

Answer is 2,047.

**Short division**

A similiar method is used here where the approximate answer is found first:

Calculate 231.3 ÷ 7

Find the approximate answer:

231.3 ÷ 7 ≈ 210 ÷ 7 = 30

Then work on the decimals

231.3 ÷ 7 = **33****.04**

**Short division by a decimal**

Calculate 58.24 ÷ 0.9 to two decimal places

Step 1 would be to write an equivalent fraction and divide by a whole number:

This is then used to find an approximate answer:

582.4 ÷ 9 ≈ 540 ÷ 9 = 60

The next step will then involve short division as we are dividing by a single digit:

58.24 ÷ 0.9 = 61**.71 (to 2 d.p.)**

**Dividing by two-digit numbers**

Calculate 76.4 ÷ 4.1

The first step would be to estimate: 76 ÷ 4 = 19

Then the equivalent calculation would be used:

76.4 ÷ 4.1 = 764 ÷ 41

Using the standard method of repeated subtraction for division, the answer: 76.4 ÷ 4.1 = **32****.37** R 0.08

** = 32.4 to 1 d.p.**

The following is another example using the repeated subtraction for division method:

Calculate 8.12 ÷ 0.46 to two decimal places

Estimate: 8 ÷ 0.5 = 16

Equivalent calculation: 8.12 ÷ 0.46 = 812 ÷ 46

Answer: 8.12 ÷ 0.43 = **17.65** R 0.1

** = 17.7 to 1 d.p.**

In this example, we multiply both numbers by 100 to make an equivalent whole number calculation.