Ratios
Understand how to compare quantities using ratios, find equivalent ratios, simplify them, and solve real-world problems.
What is a Ratio?
A ratio compares two or more quantities. It tells us how much of one thing there is compared to another.
Ratio of red to blue = 3 : 5
Read as “3 to 5” — for every 3 red items, there are 5 blue items.
Visual Example
Red : Blue = 3 : 2
Important: The order matters! Red : Blue = 3 : 2 is different from Blue : Red = 2 : 3.
Equivalent Ratios
Just like equivalent fractions, you can multiply or divide both parts of a ratio by the same number to create an equivalent ratio.
Example
2 : 3 is the same as:
Simplifying Ratios
To simplify a ratio, divide both parts by their highest common factor (HCF).
Simplify 12 : 8
Step 1: Find the HCF of 12 and 8 → 4
Step 2: Divide both: 12 ÷ 4 = 3, 8 ÷ 4 = 2
Answer: 3 : 2
Simplify 15 : 25
Step 1: HCF of 15 and 25 → 5
Step 2: 15 ÷ 5 = 3, 25 ÷ 5 = 5
Answer: 3 : 5
Ratio Word Problems
A recipe uses flour and sugar in the ratio 3 : 1. If you use 12 cups of flour, how much sugar?
Step 1: Flour part = 3, Sugar part = 1
Step 2: 12 cups flour ÷ 3 = 4 (scale factor)
Step 3: Sugar = 1 × 4 = 4 cups
Answer: 4 cups of sugar
Knowledge Check
Select the correct answer for each question. Questions get harder as you go!
Question 1
There are 4 cats and 6 dogs. What is the ratio of cats to dogs in simplest form?
Question 2
Which ratio is equivalent to 1 : 4?
Question 3
Simplify the ratio 10 : 15.
Question 4
The ratio of boys to girls in a class is 3 : 5. If there are 15 boys, how many girls are there?
Question 5
Simplify: 24 : 36
Question 6
A recipe uses butter and flour in the ratio 1 : 3. If you need 9 cups of flour, how many cups of butter do you need?
Question 7
Which of these ratios is NOT equivalent to 2 : 5?
Question 8
Sharing $48 in the ratio 3 : 5, how much does the larger share get?
Question 9
In a bag of 60 marbles, the ratio of red to green to blue is 2 : 3 : 1. How many green marbles are there?
Question 10
A map uses the scale 1 : 50,000. A road on the map is 3 cm long. What is the actual distance in metres?
Key Concepts Summary
- ●A ratio compares quantities using a colon, e.g. 3 : 5.
- ●Equivalent ratios are made by multiplying or dividing both parts by the same number.
- ●To simplify, divide both parts by their highest common factor.
- ●To share an amount, add ratio parts to find the total, then divide.
- ●Order matters: A : B is different from B : A.