Simplifying and Writing Ratios

Grade 3

What is a ratio?

A ratio compares two (or more) quantities of the same type. If a smoothie uses 3 parts mango to 2 parts banana, you write that as 3:2. The order matters — always match it to the order the question lists the quantities.

Ratios don't carry units. Once you're comparing like with like (both in grams, both in litres), the units cancel and you're left with pure numbers.

Simplifying a ratio

A ratio is in its simplest form when the numbers share no common factor other than 1. To get there, divide every part by the highest common factor (HCF).

Not sure what the HCF is? Divide by any common factor you can spot, then repeat until nothing divides cleanly. You'll arrive at the same answer.

EXAMPLE

Simplify the ratio 18:24.

The HCF of 18 and 24 is 6. Divide both parts by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. The simplified ratio is 3:4.

Writing a ratio in 1:n form

Sometimes a question asks you to write a ratio in the form 1:n. This just means making the first number exactly 1 by dividing both parts by whatever the first part currently is.

EXAMPLE

Write the ratio 5:8 in the form 1:n.

Divide both parts by 5: 5 ÷ 5 = 1 and 8 ÷ 5 = 1.6. Written in 1:n form: 1:1.6.

Watch out

Always check the units before you write a ratio. If one quantity is in centimetres and the other is in metres, convert them to the same unit first — otherwise the ratio is meaningless.

Try this one

The ratio of red to blue to yellow sweets in a bag is 4 : 5 : 1.

There are 60 sweets in total.

(a) How many blue sweets are there? [2]

(b) What fraction of the sweets are yellow? Give your answer in its simplest form. [1]

Nova's hint:

This is a three-part ratio problem combined with fractions of an amount.

Ask yourself: 'How many total parts are there, and what is one part worth?' Once you have one part, multiply by the relevant number of parts for each colour.

Try to Solve it with Nova?