Percentage: Formulas, Fraction Table and Shortcuts

Percentage is the base of profit and loss, interest, data interpretation and many word problems. If your percentage is strong, half of arithmetic becomes easy.

Basic formulas

• Percentage = (part ÷ whole) × 100.
• Percentage increase = (increase ÷ original) × 100.
• Percentage decrease = (decrease ÷ original) × 100.
• If a number increases by x% and then decreases by x%, the net change is a loss of x²/100 %.

Fraction to percentage table

• 1/2 = 50%  |  1/3 = 33.33%  |  1/4 = 25%  |  1/5 = 20%
• 1/6 = 16.67%  |  1/7 = 14.28%  |  1/8 = 12.5%  |  1/9 = 11.11%
• 1/10 = 10%  |  1/11 = 9.09%  |  1/12 = 8.33%

Successive percentage change

For two successive changes of a% and b%, the net change = a + b + (ab ÷ 100).

Example: A price rises by 20% and then by 10%. Net change = 20 + 10 + (20 × 10 ÷ 100) = 32%.

Solved examples

1. What is 15% of 240? → 0.15 × 240 = 36.
2. A number is increased from 80 to 100. Percentage increase = (20 ÷ 80) × 100 = 25%.
3. If 40% of a number is 60, the number is 60 ÷ 0.40 = 150.

Exam tips

• Use fractions instead of decimals for faster calculation.
• Check your work with the percentage calculator.
• Practise with practice papers.