# Decimals

Here we will learn about decimals including how to add decimals, subtract decimals, multiply decimals and divide decimals.

There are also decimals worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

## What are decimals?

Decimals are numbers that have parts that are not whole. Our decimal system splits whole numbers into tenths, hundredths, thousandths, and so on.

If we have a number which has tenths, hundredths etc. we can place digits corresponding to those place values after a decimal point.

E.g.

For some fractions we can find an equivalent fraction with a denominator that is a power of ten.

E.g.

### Decimal arithmetic methods

Each method of decimal arithmetic is summarised below. For detailed examples, practice questions and worksheets on each one follow the links to the step by step guides.

We can apply the four operations to decimal numbers. To do this we can apply our usual adding, subtracting, multiplying and dividing methods with a few additional steps.

E.g. Decimal subtraction

Step by step guides: Adding decimals , Subtracting decimals

E.g. Decimal multiplication

E.g. Decimal division

Step by step guide: Multiplying and dividing decimals (coming soon)

E.g. Work out

$5.68 + 7.8$

1Set up a column addition, writing one number above the other. Make sure the decimal points line up to ensure numbers in each column have the correct place value.

2Add each column from right to left remembering to carry numbers to the next column when you get a two digit number.

## How to subtract decimals

E.g. Work out

$7.5 – 3.81$

1Set up a column subtraction, writing the larger number above the other. Make sure the decimal points line up to ensure numbers in each column have the correct place value. Fill in any gaps with zeros.

2Subtract each column from right to left remembering to exchange (or borrow) from the left if required.

3Read off your answer, remembering to include the decimal point. If the original subtraction would have given a negative answer, remember to include the negative sign.

## How to multiply decimals

E.g. Work out

$5.3\times4.6$

1Multiply any decimal numbers by an appropriate power of ten to make them whole numbers.

Multiply 5.3 by 10 to make it 53 and multiply 4.6 by 10 to make it 46.

2Use column multiplication (or another preferred method) to find the product of the numbers.

$53\times46 = 2438$

3Divide the product from Step 2 by the powers of ten used in Step 1. Check that the total number of decimal digits in the question is the same as the total number of decimal digits in the answer.

In Step 1 we multiplied 5.3 by 10 and 4.6 by 10.
10 × 10 = 100 so now divide by 100.

$2438\div100 = 24.38$

Check that the total number of decimals in the question matches the total number of decimals in the answer.

## How to divide decimals

E.g. Work out

$27.12\div0.6$

1If the divisor is already an integer, you can go straight to step 3. Otherwise, write the division as a fraction with the divisor as the denominator of the fraction.

2Multiply both the numerator and denominator by the same power of 10 (or other appropriate value) to get an equivalent fraction with an integer denominator. (You can simplify the fraction further if possible to make the division easier to calculate.)

3Use short division to calculate the answer to the original division problem. If the dividend is a decimal, line up the decimal point for your quotient answer and you may need to add some trailing zeros whilst doing the division to get the correct number of decimal places.)

### Practice decimals questions

1. Work out 4.79 + 7.83

12.62

11.62

11.162

11.52

You must remember to line up the decimal points carefully and carry to the next column if the sum of the digits gives a two digit answer.

2. Work out 14.39 – 9.48

5.9

5.09

5.11

4.91

You must remember to line up the decimal points carefully and exchange (or borrow) from the left if required.

3. Multiply together 4.6 and 12.7

5842

58.42

48.42

17.3

Work out 46\times127 and then divide the answer by 100 .

4. Find the product of 5.13 and 4.9

251.37

20.117

25.137

25137

Work out 513\times49 and then divide the answer by 1000 .

5. Work out 12\div0.8

150

15

1.5

1500

Multiply both by 10 , then use short division.

6. Work out 10.2\div0.15

68

6.8

680

0.68

Multiply both by 100 , simplify the fraction by dividing both dividend and divisor by 5, then use short division.

### Decimals GCSE questions

1. You are given that 156 \times 249=38844 .
Use this information to work out the following:

(a) 15.6 \times 2.49

(b) 0.156 \times 24.9

(c) 388.44 \div 2.49

(3 marks)

(a) 38.844

(1)

(b) 3.8844

(1)

(c) 156

(1)

2. (a) If F=ma , find F , when m=4.8 and a=1.75 .

(b) If D=\frac{t}{2}-g , find D , when t=6.5 and g=1.428

(4 marks)

(a) 4.8 \times 1.75

(1)

=8.4

(1)

(b) 6.5 \div 2 (=3.25)

(1)

(1)

3. Below is the breakfast menu for a hotel.

The Smith family ordered one cooked buffet, one vegetarian buffet, three continentals, three teas and two coffees. Calculate their total bill.

(3 marks)

Calculating three teas (£ 3.60 ) or two coffees (£ 3.18 ) or three continentals (£ 14.25 )

(1)

Method to add cost of items

(1)

Correct total of £ 37.63

(1)

## Learning checklist

You have now learned how to:

• Understand and use place value for decimals, measures and integers of any size
• Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

## Still stuck?

Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.

Find out more about our GCSE maths revision programme.