Ratio explained | Primary Maths

01 What a ratio tells you — and what it does not

3 : 2 means: for every 3 parts the first one gets, the second gets 2. It says nothing about the actual amounts. The same 3 : 2 could be 3 sweets and 2 sweets, or 300 and 200.

What it does tell you is how many equal units there are altogether — 3 + 2 = 5 — and that is nearly always the way in.

Ali : Bala = 3 : 2. Five equal units in total.

02 Find one unit

Every ratio question gives you enough to work out what one unit is worth. Which fact you are given decides the first line of working.

One unit first. Ali is 3 × 40 = $120, Bala is 2 × 40 = $80.

Given the total. Total ÷ total units. If Ali and Bala share $200 in 3 : 2, that is 5 units, so one unit is 200 ÷ 5 = $40.
Given the difference. Difference ÷ difference in units. If Ali has $40 more, that gap is 3 − 2 = 1 unit, so one unit is $40.
Given one share. That share ÷ its own units. If Ali has $120, that is 3 units, so one unit is $40.
Then answer the question. Ali is 3 units, Bala is 2, the total is 5. Multiply whichever was asked for.

03 Simplifying, and why order matters

6 : 4 and 3 : 2 are the same ratio — divide both sides by 2. A ratio is in its simplest form when no number divides all its parts, exactly like a fraction.

But unlike a fraction, the order is part of the meaning. Ali : Bala = 3 : 2 is a completely different statement from 2 : 3, and writing a correct pair of numbers the wrong way round is a wrong answer.

A ratio can have more than two parts: 2 : 3 : 5 is ten units in total, shared three ways.

04 Ratio and fraction are not the same shape

This catches people constantly. In a ratio of 3 : 2, Ali's share as a fraction of the total is 3/5, not 3/2.

The ratio compares the two parts with each other. The fraction compares one part with the whole. Both are true at once, and mixing them up turns a correct model into a wrong answer.

05 How to say them

These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.

ratiosayRAY-shee-ohmore than oneratios
A comparison of two or more quantities by how many equal units each gets, written with colons: 3 : 2.
unitmore than oneunits
One equal share in a ratio. Every part of the ratio is a whole number of these.
simplest formmore than onesimplest forms
A ratio where no number divides every part. 6 : 4 simplifies to 3 : 2.
equivalent ratiosayi-KWIV-uh-luhntmore than oneequivalent ratios
A ratio meaning the same thing, made by multiplying or dividing every part equally.

06 What each level is tested on

The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.

P5
Writing and simplifying ratios, and finding one unit from a total.
Practise P5 Ratio — 10 questions →
61% of P5 papers
P6
Ratios of three quantities, ratio with fractions, and problems where a ratio changes because something is added or taken away.
Practise P6 Ratio — 10 questions →
95% of P6 papers

07 Mistakes worth knowing about

Each of these is wrong. Decide why before you open it.

“The ratio is 3 : 2, so Ali has 3 and Bala has 2.”
Only if one unit happens to be 1. The ratio gives units, not amounts — Ali could have 300 and Bala 200.
“In 3 : 2, Ali gets 3/2 of the total.”
3/5. The ratio compares Ali with Bala; the fraction compares Ali with the whole, which is 3 + 2 = 5 units.
“I wrote 2 : 3 instead of 3 : 2 — same numbers.”
Not the same statement. Order is part of a ratio's meaning, and the two describe opposite situations.
“They share $200 in 3 : 2, so one unit is 200 ÷ 3.”
Divide by the total units. 3 + 2 = 5, so one unit is 200 ÷ 5 = $40.
“Ali has $40 more, and his ratio part is 3, so one unit is 40 ÷ 3.”
The $40 is the difference, which is 3 − 2 = 1 unit. So one unit is $40 exactly.

Now try it

20 questions across 2 levels, marked as you go with the working shown.

P510 questions P610 questions