Fractions, Decimals and Percentages

Conversions to memorise

Fraction	Decimal	%
1/2	0.5	50%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
1/3	0.333…	33.3%
1/10	0.1	10%

• Fraction → decimal: divide top by bottom.
• Decimal → %: × 100. % → decimal: ÷ 100.

Four operations with fractions

• × : multiply tops, multiply bottoms: 2/3 × 4/5 = 8/15
• ÷ : Keep, Change, Flip: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
• + / − : common denominator first: 1/4 + 1/6 = 3/12 + 2/12 = 5/12

Percentage of an amount (non-calculator)

Find 15% of 80 by building blocks: 10% = 8, 5% = 4 → 12.

Percentage change

              change
% change =  ─────────── × 100
             original

£40 coat reduced to £30: change = 10 → 10/40 × 100 = 25% decrease.

Increase / decrease by a percentage (multiplier method)

• Increase by 20% → × 1.2
• Decrease by 15% → × 0.85
• Compound interest: Final = Start × (multiplier)ⁿ. £500 at 3% for 2 yrs = 500 × 1.03² = £530.45.

Reverse percentage

A price is £60 after a 20% increase. Original = 60 ÷ 1.2 = £50.

Exam tip

For "original value" (reverse %) questions, divide by the multiplier — never just take the percentage off the new price.