Numeracy, Maths and Statistics - Academic Skills Kit (2024)

ContentsToggle Main Menu 1 Definition 2 Simplifying Ratios 3 Using Ratios3.1 Worked Examples 4 Converting Between Fractions and Ratios 5 External Resources

Example 1

Simplify the ratio $16:4$.

Solution

$16$ and $4$ have a common factor of $4$; dividing through by this gives $4:1$.

Example 2

Simplify the ratio $75:45:30:60$.

Solution

There is a common factor of $5$, since each component ends in a digit $0$ or $5$. Dividing through by $5$ gives $15:9:6:12$.

The ratio can be simplified again. 3 is a factor of every component; dividing through gives the ratio $5:3:2:4$.

Note: Alternatively, if $15$ was spotted as common factor at the start, then dividing through by $15$ straight away would give the same final answer - check this for yourself.

Example 3

Write the ratio $9:14$ in the form $1:a$ where $a$ is a fraction.

Solution

This time we have to cancel the left part of the ratio down to be $1$. This is done by dividing by $9$. We must also divide the right part of the ratio by $9$ so that the parts are in the same proportion. This gives $1:\frac{14}{9}$.

Example 1

£64 is to be shared between two people, A and B, in the ratio $5:3$. Work out how much they each get.

Solution

The ratio has a total of $8$ parts since $5+3=8$.

Dividing the full amount $64$ by $8$:

\[64 \div 8 = 8\]

So each part is equal to £8.

Person A has $5$ parts, so will receive \[5 \times £8 = £40.\]

Person B has $3$ parts, so will receive \[3 \times £8 = £24\] Note: The amounts received by A and B should sum to the original amount. That is, $40+24 = 64$.

Example 2

Concrete is made by mixing gravel, sand and cement in the ratio $3:2:1$. How much gravel will be needed to make $12$m³ of concrete?

Solution

The ratio has a total of $3+2+1=6$ parts.

Divide the full amount $12$m³ by $6$:

\[12 \div 6 = 2\]

So we have six $2$m³ parts.

Gravel makes up three parts of the mixture:

\[3\times 2 = 6\text{m³}.\]

Example 3

Here is a list of the ingredients to make a quantity of houmous sufficient for 6 people.

• 2 cloves garlic
• 4 oz chick peas
• 4 tbs olive oil
• 5 fl oz tahini paste

What amounts of each ingredient would be needed so that there will be enough for 9 people?

Solution

The ratio for 6 people is $2:4:4:5$. If we divide this by $6$, we would get the ratio for one person. Then multiply by $9$ to get the ratios for $9$ people.

\begin{array}{cccccccr} 2 & : & 4 & : & 4 & : & 5 & \text{(6 people)} \\ \frac{2}{6} & : & \frac{4}{6} & : & \frac{4}{6} & : & \frac{5}{6} & \text{(1 person)} \\ \frac{2}{6} \times 9 & : & \frac{4}{6} \times 9 & : & \frac{4}{6} \times 9 & : & \frac{5}{6} \times 9 & \text{(9 people)} \\ 3 & : & 6 & : & 6 & : & 7\tfrac{1}{2} & \text{(9 people)} \\ \end{array}

So the recipe for 9 people is:

• 3 cloves garlic
• 6 oz chick peas
• 6 tbs olive oil
• 7½ fl oz tahini paste