1. What is a Ratio?
A ratio is a way of comparing one quantity to another. While a fraction compares a part to the whole, a ratio compares one part to another part (or one quantity to another quantity).
Ratio: Two or more numbers separated by a colon (:) that show the relative sizes of quantities. E.g. 3 : 2, 5 : 7 : 4
Key Understanding: In any ratio question, the thing mentioned first is associated with the first number in the ratio.
Example
A cake recipe uses flour and butter in the ratio 3 : 2
This means: flour gets "3 parts" and butter gets "2 parts"
In total, there are 3 + 2 = 5 parts
Ratios vs Fractions
Both compare quantities, but in different ways:
Fraction: Part ÷ Whole (compares to the whole)
Ratio: Part ÷ Part (compares parts to each other)
Example: A Pizza Story
A pizza is split: Person A gets 5 slices, Person B gets 3 slices (total 8)
As fractions: A has 5/8 of the pizza, B has 3/8
As a ratio: A to B is 5 : 3 (notice the 8 disappears!)
Q: A bag of sweets contains red and blue sweets in the ratio 4 : 6. What fraction of the bag is red?
2. Equivalent Ratios
Equivalent ratios are like equivalent fractions—they represent the same proportion, just written differently. You create them by multiplying (or dividing) both parts by the same number.
Equivalent Ratios: Ratios that show the same relative sizes. E.g. 2 : 3 = 4 : 6 = 10 : 15 (all scaled versions of each other)
How to Find Equivalent Ratios
Original: 2 : 3
× 5
= 10 : 15
Original: 12 : 8
÷ 4
= 3 : 2
Real-World Use: A cake recipe uses flour and butter in ratio 3 : 2. For 3g flour and 2g butter, you'd get a tiny cake! For a real cake, you'd scale up: 300g flour and 200g butter (multiply both by 100).
Examiner Tip: Always show your multiplier or divisor. Write it above/below the ratio to show your working clearly.
Q: Find an equivalent ratio to 5 : 8 where the first number is 20.
3. Simplifying Ratios
A ratio is in its simplest form when both numbers are whole numbers with no common factors (except 1). Simplifying makes ratios easier to work with and understand.
Simplified Ratio: All values are integers with no common factors. E.g. 3 : 2 is simpler than 15 : 10
How to Simplify
Divide both parts by their highest common factor (HCF). This is like reducing fractions!
45 : 30
÷ 15 (HCF)
= 3 : 2
Example: Cake Sharing
A cake is cut into 48 pieces. Amber gets 30 pieces, Naomi gets 18.
Ratio (unsimplified) = 30 : 18
HCF of 30 and 18 = 6
30 ÷ 6 = 5, and 18 ÷ 6 = 3
Simplified ratio = 5 : 3
❌ Common Mistake:
Q: Simplify the ratio 36 : 48 : 60