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Working with Ratios

Working with Ratios

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:


Which of these is not expressed as a ratio?

You can think of a ratio a bit like a fraction. 23\dfrac{2}{3} as a ratio is 2:32:3. 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 4:104:10 should be simplified to 2:52:5 by dividing each number by 2 (the HCF).

Simplify the ratio 6:186:18

Simplify the ratio 12:2412:24

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

Ann and Bert want to divide £240\pounds240 in the ratio 3:53:5. How much do they each get?


Find how much 1 part is worth

There are 3+5=83 +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×£30=£903 \times \pounds30=\pounds90.


How much does Bert get?


Great work! 👊

Ann gets £90\pounds90 and Bert gets £150\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 £9.60\pounds9.60.

Simplify the ratio 90:60:1290:60:12