2.2 Reducing a Ratio to Simplest Form
Free study material · concepts, shortcuts & solved questions
Divide both terms by their HCF.
Example 1: Reduce 45 : 60 to simplest form. HCF(45, 60) = 15. So 45 : 60 = 3 : 4.
Example 2: Reduce 2.5 : 1.5 : 3.5 to simplest form (ratio of decimals). Multiply all terms by 10: 25 : 15 : 35. Divide by HCF = 5: 5 : 3 : 7.
Example 3 (unit conversion): Find the ratio of 2 hours to 45 minutes. Convert to same unit: 2 hours = 120 minutes. Ratio = 120 : 45 = 8 : 3 (dividing by 15).
Example 3A (fractional ratio): Simplify the ratio 2/3 : 5/6. Take the LCM of denominators (3 and 6) = 6, and multiply both terms by 6: (2/3 × 6) : (5/6 × 6) = 4 : 5. Simplest form = 4 : 5.
Example 3B (decimal ratio, additional): Reduce the ratio 0.36 : 0.9 to simplest form. Multiply both terms by 100 to clear decimals: 36 : 90. HCF(36, 90) = 18. Divide: 36÷18 = 2, 90÷18 = 5. Simplest form = 2 : 5.
Example 3C (mixed-unit conversion, additional): Find the ratio of 1 hour 15 minutes to 45 minutes. Convert to the same unit: 1 hour 15 minutes = 75 minutes. Ratio = 75 : 45. HCF(75, 45) = 15. Divide: 75÷15 = 5, 45÷15 = 3. Simplest form = 5 : 3.