Percentages Made Easy: Fractions and Successive Changes

Percentages underpin profit and loss, data interpretation, interest and more. Master a few equivalents and one formula, and many questions become quick.

Fractions and their percentages

Fraction	Percentage
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%
1/12	8.33%

Use them to switch between fraction and percentage: 12.5% of 800 is 800 ÷ 8 = 100.

Finding a percentage quickly

• 10%: move the decimal one place left.
• 5%: half of 10%.
• 15%: 10% + 5%.
• 25%: divide by 4.

Example: 15% of 240 = 24 + 12 = 36.

Percentage change

Percentage change = (change ÷ original) × 100.

A price rising from 400 to 500 is 100 ÷ 400 = 25% up.

Successive changes

For two changes of a% and b%, the net change is:

a + b + (a × b) / 100 (use negatives for decreases).

• +20% then −10%: 20 − 10 − 2 = +8%.
• +10% then +10%: 10 + 10 + 1 = +21%.
• −20% then −20%: −20 − 20 + 4 = −36%.

Same percentage up and down

If a quantity rises by x% and then falls by x%, the net change is a loss of x²/100 percent.

• Up 10% then down 10%: net −1%.
• Up 20% then down 20%: net −4%.

Reversing a percentage

If a price after a 25% increase is 500, the original is 500 ÷ 1.25 = 400.

Common traps

1. Percentage of what? Always identify the base.
2. Percentage points versus percent. A rise from 10% to 15% is 5 percentage points, or 50% more.
3. Do not add successive percentages directly.

Practice

Try five short percentage questions daily. Speed comes from familiarity with the table above.

Practise with Online Exam Question & Answer →