🔢 Ratio & Proportion
A ratio compares two quantities, written a : b
▶ Play Door 10Understanding Ratio
A ratio compares two quantities. If there are 3 apples and 2 oranges, the ratio of apples to oranges is 3 : 2 (read 'three to two').
Order matters: 3 : 2 is not the same as 2 : 3. A ratio can be simplified like a fraction by dividing both parts by a common factor (6 : 4 = 3 : 2).
Worked example
Problem: There are 4 boys and 6 girls. Write the ratio of boys to girls in simplest form.
- 4 : 6 = 2 : 3 (divide both by 2).
Answer: 4 : 6 = 2 : 3 (divide both by 2).
Equivalent Ratios & Proportion
Equivalent ratios are equal in value, like equivalent fractions: 1 : 2 = 2 : 4 = 3 : 6. Multiply or divide both parts by the same number.
A proportion says two ratios are equal. If 2 pens cost ₹10, then 4 pens cost ₹20 (double the quantity, double the cost).
Worked example
Problem: Complete: 1 : 3 = 4 : ?
- Multiply both parts by 4 → 12.
Answer: Multiply both parts by 4 → 12.