Ratio and Proportion (Copy)

IGCSE CORE Mathematics Cheat Sheet: Ratio and Proportion

1. Understanding Ratio

• A ratio compares two or more quantities.
• Written as a : b or a : b : c.
• Ratios show how much of one item there is compared to another.

2. Simplifying Ratios

• Similar to simplifying fractions.
• Divide all parts of the ratio by their Highest Common Factor (HCF).

Example:
20 : 30 : 40
Divide each by 10 → 2 : 3 : 4

3. Dividing a Quantity in a Given Ratio

Steps:

1. Add the parts of the ratio.
2. Divide the total quantity by this sum to find the value of one part.
3. Multiply by each part of the ratio.

Example:
Divide 90 in the ratio 2 : 3

• Total parts = 2 + 3 = 5
• One part = 90 ÷ 5 = 18
• Share = 36 : 54

4. Using Ratios in Context

a) Adapting Recipes

If a recipe for 4 people needs 200g flour, how much for 6 people?

• 4 people : 6 people = 2 : 3
• 200g × (6 ÷ 4) = 300g

b) Map Scales

If a map scale is 1 : 50,000, then:

• 1 cm on the map = 50,000 cm in real life = 500 m

c) Best Value Problems

Compare prices to find which option gives better value.

Example:

• 5 kg for $20 → $4 per kg
• 8 kg for $30 → $3.75 per kg (better value)

5. Proportion

• Two quantities are in proportion if they increase/decrease at the same rate.
• Use cross multiplication to solve proportion problems.

Example:
If 3 pens cost $6, how much do 5 pens cost?

3 pens : 5 pens = $6 : x
Cross multiply:
3x = 30 → x = $10

6. Direct and Inverse Proportion

• Direct Proportion:
  When one quantity increases, the other increases.
  x ∝ y
• Inverse Proportion:
  When one quantity increases, the other decreases.
  x ∝ 1/y

7. Examples

• Simplify 45 : 60 → divide by 15 → 3 : 4
• Divide 150 in ratio 3 : 2
  Total parts = 5
  One part = 150 ÷ 5 = 30
  Share = 90 : 60
• A car travels 120 km in 2 hours. How far in 5 hours (same speed)?
  120 ÷ 2 = 60 km/h
  60 × 5 = 300 km

8. Quick Reference Table

9. Tips for Exams

• Always simplify ratios unless told otherwise.
• When dividing quantities, ensure you add parts correctly.
• Use proportion for scaling problems—especially recipes, maps, and speed.
• For best value, divide price by quantity to compare.
• Recognize whether the situation is direct or inverse proportion.