Ratio
Equivalent ratios, simplest form, ratios of two and three quantities, dividing an amount in a ratio, and relating ratio to fractions.
⏱ 8 min · 🎯 5 things to master
A ratio is how we compare amounts without giving the exact numbers — like a recipe that says "mix water and syrup in the ratio 1 to 4", or how a class shares chores. It tells you the proportion, not the total. Once you see a ratio as a set of equal units, dividing money or mixing drinks becomes simple. Let's pour into it.
Parents: let your child predict before they reveal each step. The blue dotted words are tappable definitions, and the "Method tip" boxes name exactly what a PSLE marker rewards in the working — not just the final number.
By the end you'll be able to write equivalent ratios, simplify to simplest form, handle two and three quantities, divide an amount in a ratio, and link ratio to fractions. Let's begin.
Equivalent ratios
A compares amounts. Two ratios are when you multiply or divide both sides by the same number. So 1 to 2 is the same comparison as 2 to 4 and 3 to 6 — each just scaled up.
Think of orange squash mixed 1 part syrup to 3 parts water. If you make a bigger jug with 2 parts syrup, you need 6 parts water to keep the same taste — that is 2 to 6, equivalent to 1 to 3.
🤔 Predict first: Which ratio is equivalent to 2 to 5?
Simplest form
A ratio is in its when both sides share no common factor except 1. To simplify, divide both sides by their greatest common factor. So 6 to 9 divides by 3 to give 2 to 3, which cannot go smaller.
Simplifying a ratio is exactly like simplifying a fraction — find the largest number that divides both sides and use it.
🤔 Predict first: What is 8 to 12 in its simplest form?
Ratio of three quantities
A ratio can compare three amounts at once, like the chocolate, vanilla and strawberry scoops sold at a shop: 4 to 3 to 5. The same rules apply — to simplify, divide all three parts by their common factor; to scale up, multiply all three.
So 6 to 9 to 12 simplifies by dividing each part by 3, giving 2 to 3 to 4. Keep the order the same and treat all three parts together.
🤔 Predict first: What is 4 to 6 to 10 in its simplest form?
Dividing an amount in a ratio
To split an amount in a ratio, first add the parts to find the total number of units, then find one unit. Share $40 between Ali and Bala in the ratio 3 to 5. The total is 3 + 5 = 8 units, so one unit is 40 ÷ 8 = $5. Ali gets 3 × 5 = $15 and Bala gets 5 × 5 = $25.
Check it: 15 + 25 = 40. This unit method works for any sharing problem and is the heart of ratio at PSLE.
🤔 Predict first: $60 is shared in the ratio 1 to 2. What is the larger share?
Relating ratio to fractions
A ratio and a fraction are linked. If sweets are shared red to green in the ratio 2 to 3, then there are 5 parts in all, so the red sweets are two fifths of the total and green are three fifths. The bottom of the fraction is the total number of parts.
This link is powerful: a question might give you a fraction and ask for the ratio, or the other way around. If one third of the class are boys, then boys to girls is 1 to 2, because the remaining two thirds are girls.
🤔 Predict first: In a box, the ratio of apples to oranges is 3 to 2. What fraction of the fruit are apples?
Watch out — these are easily mixed up
Quick recap
🎯 Mastery check
Answer all 6 — your progress is saved on this device.
Which ratio is equivalent to 3 to 4?
What is 10 to 15 in its simplest form?
What is 6 to 9 to 15 in its simplest form?
$72 is shared between two children in the ratio 4 to 5. What is the smaller share?
The ratio of boys to girls in a club is 2 to 3. What fraction of the club are girls?
A drink mixes syrup and water in the ratio 1 to 4. If you use 3 cups of syrup, how many cups of water do you need?