# Functional Skills: Ratio

## Functional Skills: Ratio Revision

**Ratio**

A **ratio** is something we use to compare how much there is of one thing to how much there is of another.

A **ratio** is written like **2:5** and is spoken as **“****2 to 5****”**. This means that for every 2 lots of one thing, there must be 5 lots of the other.

There are **3** skills you need to know for **ratios**.

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

**Skill 1: Simplifying Ratios**

To **simplify** a ratio, **divide** each part of the ratio by the same number each time, until they can no longer be divided.

**Example:** Write the ratio \textcolor{red}{18}:\textcolor{blue}{60}:\textcolor{limegreen}{24} in its **simplest form**.

We can divide each number by 3 and then by 2 (or just by 6):

This cannot be simplified anymore to make whole numbers, so the ratio is in its **simplest form**, which is \textcolor{red}{3}:\textcolor{blue}{10}:\textcolor{limegreen}{4}

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**Skill 2: Solving Questions Involving Ratios**

There are various types of questions involving **ratios** that you will encounter.

**Example:** Olive makes her tea by adding \textcolor{blue}{1} part milk to \textcolor{red}{7} parts hot water (\textcolor{blue}{1} : \textcolor{red}{7}). If Olive uses 30 ml of milk, how much hot water does she use?

The amount of milk used is \text{\textcolor{blue}{1 part}} = \textcolor{blue}{30 \text{ ml}}

Olive uses 7 parts of hot water to every part of milk.

So,

The amount of hot water used is \textcolor{red}{\text{7 parts}} = \textcolor{red}{7} \times \textcolor{blue}{30} = \textcolor{black}{210 \text{ ml}}

**Example:** Simon and Luca sell some items at an auction. They make £450 in total.

They split the money they make respectively in the ratio \textcolor{red}{4}:\textcolor{limegreen}{5}. Work out how much money each of them receive.

The ratio tells us that there are

\textcolor{red}{4} + \textcolor{limegreen}{5} = 9 parts

\textcolor{red}{4} of these go to Simon and \textcolor{limegreen}{5} of these go to Luca.

So, find how much \textcolor{purple}{1} part of £450 is worth, by dividing the total number of parts, 9

\textcolor{purple}{\text{1 part}} = £450 \div 9 = \textcolor{purple}{£50}

So,

\text{Simon's share} = \textcolor{red}{4 \text{ parts}} = \textcolor{red}{4} \times \textcolor{purple}{£50} = \textcolor{black}{£200}

\text{Luca's share} = \textcolor{limegreen}{5 \text{ parts}} = \textcolor{limegreen}{5} \times \textcolor{purple}{£50} = \textcolor{black}{£250}

**Skill 3: Calculating Total Amounts**

You can use ratios to calculate **total amounts**, using the following steps:

**Step 1:** Calculate the value of one part (you may be given this in the question).

**Step 2:** Calculate the total number of parts.

**Step 3:** Calculate the total amount, by multiplying the value of one part by the total number of parts.

**Example:** A basic dough is made by mixing \textcolor{blue}{3} parts of Greek yoghurt and \textcolor{limegreen}{4} parts self-raising flour.

160 g of self-raising flour is used. How much dough is made in total?

4 parts self-raising flour is 160 g, so

\textcolor{purple}{\text{1 part}} = 160 \div 4 = \textcolor{purple}{40 \text{ g}}

The total number of parts is

\textcolor{blue}{3} + \textcolor{limegreen}{4} = \textcolor{red}{7}

So, the total amount of dough made is

\textcolor{red}{7} \times \textcolor{purple}{40 \text{ g}} = \textcolor{black}{280 \text{ g}}

## Functional Skills: Ratio Example Questions

**Question 1:** There are 160 men and 280 women in a crowd. What is the ratio of men to women, in its simplest form?

**[1 mark]**

The ratio of men : women is 160 : 280

This can be simplified, by dividing both sides by 10:

16:28

it can be simplified further, by dividing both sides by 4:

4:7

This can no longer be divided to make whole numbers, so it is in its simplest form.

**Question 2:** Liam makes fruit squash by adding 5 parts of water to 1 part of squash. How much water would he used if he used 50 ml of squash?

**[2 marks]**

The amount of squash used is 1 part = 50 ml

Liam uses 5 parts of water to every part of squash.

So, the amount of water needed is

5 \times 50 ml = 250 ml

**Question 3:** Adam, Ben and Charlie are three brothers. The brother’s ages added together is 63. The ratio of their ages is 3:4:2. How old is each brother?

**[2 marks]**

The total number of parts in the ratio is

3 + 4 + 2 = 9

1 part is worth

63 \div 9 = 7 years

Adam’s part of the ratio is 3 parts, so he is

3 \times 7 = 21 years old

Ben’s part of the ratio is 4 parts, so he is

4 \times 7 = 28 years old

Charlie’s part of the ratio is 2 parts, so he is

2 \times 7 = 14 years old

**Question 4:** Jamie makes some fudge using 2 parts of chocolate to 3 parts of frosting.

330 g of frosting is used. How much fudge is made in total?

**[2 marks]**

1 part = 330 \div 3 = 110 g

Total number of parts = 2 + 3 = 5

Total amount of fudge made = 5 \times 110 g = 550 g

## Functional Skills: Ratio Worksheet and Example Questions

### Ratio L1, L2

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