What is a Ratio?
A ratio is a comparison between two or more quantities of the same kind. It tells us how much of one thing there is compared to another.
Ratios appear all around us in everyday life — the ratio of boys to girls in a class, the ratio of flour to sugar in a recipe, or the ratio of distances on a map compared to real life.
A ratio can be written in several ways:
- Using a colon: 3 : 2
- As a fraction: 3/2
- In words: "3 to 2"
Example: A smoothie recipe uses 3 cups of fruit and 2 cups of yoghurt.
The ratio of fruit to yoghurt is 3 : 2.
This means for every 3 cups of fruit, you use 2 cups of yoghurt. If you doubled the recipe, you would use 6 cups of fruit and 4 cups of yoghurt — the ratio stays the same: 6 : 4 = 3 : 2.
Always check what the ratio is comparing — order matters! A ratio of 3 : 2 (fruit to yoghurt) is not the same as 2 : 3 (yoghurt to fruit).
Simplifying Ratios
Just like fractions, ratios can be simplified by dividing both parts by their highest common factor (HCF).
The largest number that divides exactly into two or more numbers.
A ratio is in its simplest form when both numbers share no common factor other than 1.
Example: Simplify the ratio 12 : 8.
Step 1: Find the HCF of 12 and 8.
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 8: 1, 2, 4, 8
- HCF = 4
Step 2: Divide both parts by 4.
So 12 : 8 = 3 : 2 in simplest form.
You must divide both parts of the ratio by the same number. If you only divide one side, the ratio changes meaning entirely!
Students sometimes add or subtract to simplify ratios. Remember — you must multiply or divide both parts by the same number, never add or subtract.
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