Sheet 2 of 10 · Maths

Fractions, decimals and percentages

Key equivalents, percentages of amounts and working with fractions. 8 rules, each with a worked example.

Key equivalents

Must-know equivalents
½ = 0.5 = 50% · ¼ = 0.25 = 25% · ¾ = 0.75 = 75%
- ⅕ = 0.2 = 20% · ⅒ = 0.1 = 10% · ⅛ = 0.125 = 12.5%
- ⅓ = 0.333… ≈ 33.3% · ⅔ = 0.666… ≈ 66.7%
Tip: Per cent means “out of 100”.
Converting
Fraction → decimal: top ÷ bottom · Decimal → %: × 100
Example⅜ = 3 ÷ 8 = 0.375 = 37.5%

Percentage of an amount
Find 10% (÷ 10), then build up
- 1% = ÷ 100 · 5% = half of 10% · 50% = ÷ 2
Example35% of 60: 10% = 6, so 30% = 18 and 5% = 3; 18 + 3 = 21
Increase and decrease
Find the percentage, then add it on (increase) or take it off (decrease)
Example£80 up by 15%: 15% = £12, so £92 · £40 coat with 25% off: 25% = £10, so £30

Fraction of an amount
Divide by the bottom, multiply by the top
Example⅗ of 45: 45 ÷ 5 = 9, then 9 × 3 = 27
Simplifying
Divide the top and bottom by the same number (the HCF)
Example18/24: both divide by 6, so 18/24 = 3/4
Comparing fractions
Make the denominators the same, then compare the numerators
Example⅔ or ¾? ⅔ = 8/12 and ¾ = 9/12, so ¾ is bigger
Improper fractions and mixed numbers
Improper → mixed: divide, and the remainder goes on top
- Mixed → improper: whole number × bottom, + top
Example17/5 = 3⅖ (17 ÷ 5 = 3 r 2) · 2¾ = 11/4 (2 × 4 + 3 = 11)

The study guide goes through each rule step by step, with more examples.