Comparing quantities
A ratio compares quantities. If a bag has 3 red marbles and 5 blue marbles, the ratio of red to blue is 3 to 5.
Three ways to write a ratio
| Form | Example |
|---|---|
| Words | 3 to 5 |
| Colon | 3:5 |
| Fraction | 3/5 |
Each number is a term of the ratio.
Order matters
The order of the terms follows the order of the words.
- Red to blue = 3:5
- Blue to red = 5:3
These are different ratios!
Types of ratios
| Type | Compares | Marbles example |
|---|---|---|
| Part-to-part | one part to another | red : blue = 3:5 |
| Part-to-whole | one part to the total | red : all = 3:8 |
| Whole-to-part | the total to a part | all : blue = 8:5 |
Part-to-whole ratios are also fractions: 3/8 of the marbles are red.
Ratios with more than two terms
A fruit salad has 2 cups of apples, 3 cups of grapes and 1 cup of melon. The ratio apples:grapes:melon is 2:3:1.
Ratios have no units
If the quantities have the same unit, the units cancel. A 2 m board and a 50 cm board: first convert to the same unit (200 cm and 50 cm), then 200:50 = 4:1.
Where you see ratios
- Recipes: 2 cups flour to 1 cup sugar
- Maps: 1:50,000
- Screens: 16:9
- Sports: wins to losses, 12:4
- Mixing paint or juice concentrate: 1 part concentrate to 3 parts water
Worked examples
Example 1: A class has 12 boys and 15 girls. Write the ratio of girls to boys.
15:12 (which simplifies to 5:4).
Example 2: What is the ratio of boys to all students?
12:27 (= 4:9).
Example 3: A team won 9 games and lost 6. Write the ratio of losses to wins.
6:9 (= 2:3).
Common mistakes
- Writing the terms in the wrong order.
- Confusing part-to-part with part-to-whole.
- Comparing quantities in different units without converting.
Try it yourself
A box has 4 pencils, 6 pens and 2 markers.
- Ratio of pencils to pens.
- Ratio of markers to all items.
- Ratio of pens to pencils to markers.
- Write pencils : all items as a fraction.
Answers: 1) 4:6 (2:3) 2) 2:12 (1:6) 3) 6:4:2 (3:2:1) 4) 4/12 = 1/3
Quick recap
- A ratio compares quantities: words, colon or fraction form.
- Order matters.
- Ratios can be part-to-part or part-to-whole.