Percentages

What is a Percentage?

Percent means 'out of 100'. So 45% = 45/100 = 0.45

Converting Between Forms

Fraction → %: multiply by 100  |  % → decimal: divide by 100

Finding a Percentage of a Quantity

Convert the percentage to a decimal, then multiply.

Example: 35% of 240 = 0.35 × 240 = 84

Mental shortcut: 10% first, then scale.
10% of 240 = 24, so 35% = 3 × 24 + 5% of 24 = 72 + 12 = 84

Percentage Increase and Decrease

Increase by %: Multiply by (1 + rate)
Increase $200 by 15% → 200 × 1.15 = $230

Decrease by %: Multiply by (1 − rate)
Decrease $200 by 15% → 200 × 0.85 = $170

Percentage Change Formula

% change = (Change ÷ Original) × 100

Example: Price increases from $80 to $100.
% increase = (20 ÷ 80) × 100 = 25%

Finding the Original Value

If a value after a percentage change is given, reverse the operation.

Example: After a 20% increase, the price is $120. What was the original?
Original × 1.20 = 120 → Original = 120 ÷ 1.20 = $100

Key Tips

• GST problems: GST is 10%, so price with GST = original × 1.10
• Discount problems: look for 'original price' vs 'sale price'
• Common percentages to memorise: 12.5% = 1/8, 33.3% ≈ 1/3, 66.7% ≈ 2/3