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Cambridge / IGCSE • Number & Arithmetic

Ratios and Percentages

Ratios and percentages help us compare quantities in real-world scenarios, from calculating discounts to scaling recipes.

Learning Objectives

  • Express quantities as ratios in simplest form
  • Divide a quantity into a given ratio
  • Calculate percentage increases and decreases

Lesson Explanation

Lesson Content

A ratio compares two or more quantities of the same unit. To simplify a ratio, divide all terms by their highest common factor (HCF). A percentage is a fraction out of 100.

💡 Key Takeaway

Take one step at a time, check your working carefully, and keep both sides balanced!

Worked Examples

Example 1

Simplify the ratio 12 : 18

  1. Step 1

    Find the highest common factor of 12 and 18, which is 6

  2. Step 2

    Divide both numbers by 6: 12 ÷ 6 = 2, 18 ÷ 6 = 3

  3. Step 3

    Simplified ratio: 2 : 3

Example 2

Divide $50 in the ratio 2 : 3

  1. Step 1

    Total parts = 2 + 3 = 5

  2. Step 2

    Value of 1 part = $50 ÷ 5 = $10

  3. Step 3

    First share (2 parts) = 2 × $10 = $20

  4. Step 4

    Second share (3 parts) = 3 × $10 = $30

Visual Method

Balance Every Step

Mathematics becomes much clearer when you can see the structure behind equations.

Watch Video Explanation

Practice Questions

Try solving each question on paper first. Tap below to check a helpful hint or solution!

Question 1

Simplify the ratio 15 : 25 : 35

Show Hint / Solution 💡

Divide all three numbers by 5.

Question 2

Divide 40kg in the ratio 3 : 5

Show Hint / Solution 💡

Find total parts (3 + 5 = 8), then calculate value per part.

Question 3

Increase $80 by 15%

Show Hint / Solution 💡

Calculate 15% of $80 ($12), then add it to $80.

Lesson Summary

What to Remember

Ratios compare parts to parts, while percentages express values out of 100.

Download Lesson Notes ↓