Recap: Percentages

Here you know the old figure and the new figure, and want the change as a percentage.

• Step 1: find the change, which is the gap between the new figure and the old one
• Step 2: divide the change by the old figure
• Step 3: multiply by 100

Worked example: a tin of paint goes from £20 to £25. The change is £5. 5 ÷ 20 = 0.25, and × 100 gives an increase of 25%.

Always divide by the old figure, never the new one.

The original amount is 100% of itself. After a 20% increase, the new amount is 120% of the original.

• Step 1: add the percentage rise to 100, then divide by 100. A 20% rise gives 1.2
• Step 2: divide the new amount by that figure

Worked example: a price is £60 after a 20% rise. 60 ÷ 1.2 = £50. Check: 20% of £50 is £10, and adding it gives £60.

The original amount is 100% of itself. After a 20% increase, the new amount is 120% of the original.

• Step 1: add the percentage rise to 100, then divide by 100. A 20% rise gives 1.2
• Step 2: divide the new amount by that figure

Worked example: a price is £60 after a 20% rise. 60 ÷ 1.2 = £50. Check: 20% of £50 is £10, and adding it gives £60.

Per cent means out of 100. So 15% is 15 out of every 100.

• Step 1: divide the percentage by 100 to get a decimal
• Step 2: multiply the amount by that decimal

Worked example: 15% of £240. 15 ÷ 100 = 0.15. Then 240 × 0.15 = £36.

It is tempting to take the same percentage off the new price. That gives the wrong answer.

The rise was worked out on the old price. Taking the percentage off the new price works it out on a bigger figure, so it takes off too much.

A sander costs £90 after a rise of 25%. Priya takes 25% off £90 and gets £67.50.

A price rise or a pay rise is often given as a percentage. So is a price cut.

• Step 1: work out the percentage of the amount
• Step 2: add it for an increase, or take it away for a decrease

Worked example: a drill costs £80 and goes up by 5%. 5% of £80 is £4. The new price is £80 + £4 = £84.