Fractions in Disguise

Overview

This chapter looks at fractions appearing in different forms — equivalent fractions, decimals, percentages and ratios — and how to convert between them. It strengthens operations with fractions and their real-life uses.

Key concepts

• Equivalent fractions name the same value, e.g. 1 ÷ 2 = 2 ÷ 4 = 50%.
• A fraction can be written as a decimal by dividing numerator by denominator.
• Percent means out of 100; a fraction times 100 gives the percentage.
• To add or subtract fractions, use a common denominator.

Important formulae

• (a ÷ b) × (c ÷ d) = (a × c) ÷ (b × d)
• (a ÷ b) ÷ (c ÷ d) = (a ÷ b) × (d ÷ c)
• Fraction to percent: (a ÷ b) × 100.

Solved example

1. Express 3 ÷ 8 as a decimal and a percentage.
2. Divide: 3 ÷ 8 = 0.375.
3. Multiply by 100: 0.375 × 100 = 37.5%.

Important questions

1. Write three fractions equivalent to 4 ÷ 5.
2. Convert 0.65 into a fraction in lowest terms.
3. Add 2 ÷ 3 and 3 ÷ 4.
4. What is 15% of 240 written as a fraction of the whole?

Quick revision

Fractions, decimals, percentages and ratios are four disguises of the same quantity — learn to switch freely. Simplify by dividing top and bottom by their HCF, and always use a common denominator when adding or subtracting.