Functional Skills: Ratio

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 $textcolor{red}{3}:textcolor{blue}{10}:textcolor{limegreen}{4}$

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

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