Work back to the original amount after a percentage change, take VAT off, combine two changes and compare deals.
What you will learn
- Find the original amount after an increase or decrease
- Remove VAT from a price
- Combine two percentage changes
- Compare offers
Work backwards with the multiplier
After a 20% discount, a price is 80% of the original.
So divide by 0.8, do not add 20% back.
- sale price £36 after 20% off
- £36 is 80% of the original
- original = £36 ÷ 0.8 = £45
Check: 20% of £45 is £9, and £45 − £9 = £36. Adding 20% of £36 gives £43.20, which is wrong, because the 20% was of the original.
Prices with VAT at 20% are 120% of the price without: divide by 1.2. After any increase, divide by its multiplier: a town that grew by 4% to 13,000 people had 13,000 ÷ 1.04 = 12,500 before.
If you know a percentage of a number, find 1% first. 15% of a number is 60: 1% is 60 ÷ 15 = 4, so 100% is 400.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Work backwards with the multiplier
- Two changes in a row
- Try it: Undo a discount
7 practice questions, marked as you go; about 25 minutes in all.
In this unit: Fractions, decimals and percentages
Calculate with fractions and mixed numbers, move between fractions, decimals and percentages, and solve percentage problems, including reverse percentages.
- Working with fractions
- Multiplying and dividing fractions
- Fractions, decimals and percentages
- Percentages
- Reverse percentages and repeated change