Number

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Working with Ratios

Ratios allow us to divide quantities into different amounts, and see the value of these quantities relative to each other.

A ratio is a way of dividing a quantity into different amounts, and allows us to easily visualise their value relative to each other.

Ratios are written as two numbers on opposite sides of a colon. In general, they mean that for every amount of units on the left, there are the amount of units on the right. Here's an example:

$8:10$

Which of these is not expressed as a ratio?

You can think of a ratio a bit like a fraction. $\dfrac{2}{3}$ as a ratio is $2:3$ . This means that for every 2 units on the left, there are 3 units on the right.

Like a fraction, a ratio should simplified and written in its lowest terms. A ratio of $4:10$ should be simplified to $2:5$ by dividing each number by 2 (the HCF).

Simplify the ratio $6:18$

Simplify the ratio $12:24$

Often, we look to divide a quantity in a certain ratio.

Ann and Bert want to divide $\pounds240$ in the ratio $3:5$ . How much do they each get?

Find how much 1 part is worth

There are $3 +5=8$ parts in total, so we can find the value of 1 part by dividing 240 by the number of parts.

What is one part worth?

Work out how much Ann gets

Ann gets 3 parts of the total. Therefore, she gets $3 \times \pounds30=\pounds90$ .

How much does Bert get?

Great work! 👊

Ann gets $\pounds90$ and Bert gets $\pounds150$ . We can't be sure whether Bert deserved this...

Share 360 in the ratio 4:5, giving your answer as a ratio containing the full amounts.

If there are 3 parts to the ratio, the method is the same.

Mark is 13 years old, Becky is 12 years old, Dave is 10 years old. Mark, Becky and Dave share £28 in the same ratio as their ages. How much should Becky have?

What is 1 part worth?

How much should Becky receive?

Nice! 🤟🏼

Becky should receive $\pounds9.60$ .

Simplify the ratio $90:60:12$