1. Percentages and Proportional Change
CHAPTER 17 Unit C
Percentages and Proportional Change

2. C17.1 Percentage increase and decrease
Percentage increase When we increase an amount by a certain percentage we do the following. For example: Increasing £10.00 by 25% we would find 25% of £10.00 by doing £10.00 x 25 / 100 = £2.50 And then we would add this to the original 100% value of £ Giving us a total of £12.50

3. Using a multiplier
Using multiplier can make it easier for us. We can increase £10.00 by 25% by simply doing: £10.00 x 1.25 = £12.50 Notice that we multiply by 1. %increase Amount X 1.(%increase) = increased value

4. Work out the multiplier in these
X 1.50
50% increase
33% increase
2% increase
88% increase
X 1.33
x1.02
x1.88

5. Sample question using percentage increase
Harry’s salary is £38,000. It increases by 4% Work out his new salary.
£38,000 x 1.04 = £39,520

6. Making a profit
When we sell things we make a profit. For example: Orange squash cost £1.00 Selling price £1.50 We have made a profit of £0.50 If we divide £1.50 by £1.00 we 1.50 which means that the multiplier is 1.50 Hence this is a 50% profit made on the orange

7. Practice question £40 x 1.35 = £54
Work out the sale price of a mobile phone bought at £40 and sold at a 35% profit.
£40 x 1.35 = £54

8. Percentage reduction
Often things reduce in value. For example in a sale, prices are reduced. Also when things get old their value depreciates. A camera that cost £540 is reduced by 24% in a sale. What is the new price? Firstly we need to find 24% of £540 £540 x 24/100 = £ And then take this away from the original 100% of £540. £540 - £ = £410.40

9. Using multipliers
Using a multiplier can make things easier. So for example if reduce £540 by 24% we will be left with 76% of the original amount. 100% - 24% = 76% Therefore we can simply do the following: £540 x 0.76 = £ Amount x 0.(100%- % reduction) = reduced value

10. Work out the multiplier

11. Work out the multiplier in these
X 0.50
50% decrease
33% decrease
2% decrease
88% decrease
X 0.67
X 0.98
X0.12

12. finding out what percentage increase or decrease has occurred
Divide the new price by the original.
For example, the cost of a painting went from £35.00 to £66.15 in one year. What was the percentage increase?
Answer:  35 = 1.89
This indicates a percentage increase of 89 %

13. A car went down from £4200 to £2814 in 3 years
A car went down from £4200 to £2814 in 3 years. What percentage reduction was this?
New / old
2814  4200 = 0.67
This indicates a reduction of 33%.
Remember to subtract from 1 whole.
(1 – 0.67 = 0.33)