A ratio compares two or more quantities. Ratios are everywhere — in recipes, maps, mixing paints, and sharing things fairly. Understanding ratios helps you solve real-world problems!
📝 What is a Ratio?
Writing Ratios
If there are 3 apples and 2 oranges, the ratio of apples to oranges is:
- 3 : 2 (using a colon)
- 3 to 2 (using words)
- 3/2 (as a fraction)
Order matters! 3:2 is different from 2:3
🍰 Real Life Examples
1 : 2
Cordial mix (1 part cordial, 2 parts water)
1 : 100,000
Map scale (1cm = 1km)
3 : 1
Concrete mix (3 parts gravel, 1 part cement)
➗ Simplifying Ratios
Like Fractions!
Divide both parts by their highest common factor:
- 12 : 8 → divide by 4 → 3 : 2
- 15 : 25 → divide by 5 → 3 : 5
📐 Scaling Up and Down
A recipe uses flour to sugar in ratio 3:1 and makes 12 muffins.
Q: How much flour for 36 muffins?
Method: 36 ÷ 12 = 3 (scale factor)
If original flour was 150g: 150 × 3 = 450g flour
🍕 Sharing in a Ratio
Worked Example
Share $60 in the ratio 2:3
- Total parts = 2 + 3 = 5
- One part = $60 ÷ 5 = $12
- First share = 2 × $12 = $24
- Second share = 3 × $12 = $36
✏️ Activities
Practice Problems
- Simplify 20:15 = ___:___
- A class has 12 boys and 18 girls. What is the ratio boys:girls in simplest form? ___:___
- Share $100 in the ratio 3:2. First person gets $___ Second gets $___
My working:
👩🏫 Teacher Notes
Curriculum Links
- Mathematics: Number — ratios, proportional reasoning