# Decimals

## Decimals Revision

**Decimals**

A **decimal** is a number in between two whole numbers.

For example: the decimal 4.5 is between the whole numbers 4 and 5

**Decimals** have numbers to the right of a decimal point.

All of these are examples of decimals: 3.6, 4.98, 8.546

Make sure you are happy with the following topics before continuing:

**The Four Operations**

We can use the four operations (addition, subtraction, multiplication and division) with decimals, and using our calculator, the method is the same.

**Addition**:

Just as before, addition can be done by typing equations into your calculator, for example:

4.6+5.9=10.5

**Subtraction**:

Similarly to addition, we can use our calculator to work out **subtraction** questions, for example:

By typing in 13.8-11.1, our calculator would give the solution, 2.7.

**Multiplication**:

Again, we can use our calculator to work out **multiplication** questions:

If we had to multiply 3.7 by 2.8, we would type in 3.7\times2.8, and the calculator would output 10.36.

**Division**:

And finally, we can use our calculator to work out **division** questions, for example:

60 divided by 1.5 would be calculated by typing in 60\div1.5, giving the answer 40.

As explained in **The Four Operations**, there may be simple operation questions, or more complicated, applied questions. These will be covered in the example questions.

**Example 1: Simple Operations**

Use your calculator to work out these four operation questions:

a) 1.35+1.6+1.89

b) 100.5-6.8-5.99

c) 2.1\times3.6\times4.5\times1.2

d) 364\div3.5\div5.2

**[4 marks]**

a) By typing the sum into a calculator:

1.35+1.6+1.89=4.84

b) By typing the sum into a calculator:

100.5-6.8-5.99=87.71

c) By typing the sum into a calculator:

2.1\times3.6\times4.5\times1.2=40.824

d) By typing the sum into a calculator:

364\div3.5\div5.2=20

**Example 2: Applied Operations**

Hugo is going to a supermarket. He buys broccoli for \text{£}1.10, a bag of carrots for \text{£}0.89 and 12 potatoes each priced at \text{£}0.38.

By using multiplication and addition, calculate how much money Hugo spent overall at the supermarket.

**[3 marks]**

Firstly, we can work out how much he spent in total on potatoes by **multiplying** the price by the number of potatoes bought:

Now, we can **add up** everything he bought to find his total:

## Decimals Example Questions

**Question 1: **Bradley went to the pet shop. He bought a lizard for \text{£}120.99, some lizard food for \text{£}5.99, and a terrarium for \text{£}210.70.

How much did he spend in total?

**[2 marks]**

We can solve this using addition on our calculator:

\text{£}120.99+\text{£}5.99+\text{£}210.70=\text{£}337.68**Question 2: **Richard was asked to go to the supermarket by his mum, she gave him a \text{£}10 note to buy bread, milk, and eggs. The bread cost \text{£}1.39, the milk cost \text{£}1.20, and the eggs cost \text{£}3.79.

Calculate how much change Richard would have left to give back to his mum.

**[4 marks]**

We can solve this problem using subtraction on our calculator:

\text{£}10-\text{£}1.39-\text{£}1.20-\text{£}3.79=\text{£}3.62**Question 3: **Ben, Billy, and Bob planned a picnic at the park. For their picnic, they went to the supermarket and bought 6 pink doughnuts which were \text{£}0.79 each, 12 cans of fizzy drinks for \text{£}0.99 per can, 3 bananas for \text{£}0.99 each, and finally, 2 Caesar salads for \text{£}3.99 each.

They paid for this shopping, splitting the overall cost equally between each of the boys. How much did Ben spend?

**[4 marks]**

Pink doughnuts:

6\times\text{£}0.79=\text{£}4.74

Fizzy drinks:

12\times\text{£}0.99=\text{£}11.88

Bananas:

3\times\text{£}0.99=\text{£}2.97

Caesar salads:

2\times\text{£}3.99=\text{£}7.98

Total:

\text{£}4.74+\text{£}11.88+\text{£}2.97+\text{£}7.98=\text{£}27.57We can divide this total by 3 to see how much Ben spent:

\text{£}27.57\div3=\text{£}9.19