1. Ratio and Percentages

2. Percentage/Decimal/Fraction
These are different ways of saying how much of something you have
E.g. 100% = 1.0 = 1
50%= 0.5 = ½
What is 25%?
0.25 and ¼
What is 10%?
0.1 and 1/10

3. Percentage/Decimal/Fraction
What is 1/3?
33.3% and 0.33
What is 2/3?
66.67% and 0.67
What is 150%?
1 ½ and 1.5
What is 7%?
0.07 and 7/100

4. Simplifying Fractions
Fractions should always be simplified
E.g. 2/4 is ½
What are these:
10/100?
1/10
2/100?
1/5
4/6?
2/3

5. Try these Change these percentages to fractions: 70% 5% 15% 2% 12 ½ %
6 ¼ %
66 2/3 %

6. Answers 7/10 5/100 which is 1/20 15/100 which is 3/20
1/8
1/16
2/3

7. Converting Fractions to Percentages
To convert a fraction into a percentage there are two ways:
Type the fraction into your calculator and multiply by 100
Divide the top part of the fraction by the bottom part and multiply by 100 e.g.
½ is ½ x 100 = 50%
¼ is
25%

8. Try these Convert these fractions to percentages: 71/80 4/5 56/60
16/40
23/28
112/125

9. Answers
88.75%
80%
93.3%
40%
82.1%
89..6%

10. Sales Often sales are 25% off or 50% off
This means you can work out what the sale price is
E.g. If a football costs £12 and there is 25% off
You type in 12 x 25% on your calculator
This is £3
The football is £12-3 = £9

11. Work out these:
What are the prices of these if there is a 25% off sale;
A £6 football pump
£7 tennis balls
£20 fishing rod
If there is 10% off these;
£108 tent
£12 airbed
£16 gas cooker

12. Answers
£4.50
£5.25
£15
£97.20
£10.80
£14.40

13. Working out the % of something
If you are asked to find the percentage of something e.g. 12% of 300g
Type 300 x 12% into the calculator
36g
There is another method
300 ÷ 100 gives you 1%, then multiply your answer by 12
300 ÷ 100 = 3g
3g x 12 = 36g

14. Try these Find 18% of 250cm Find 8% of 600cm Find 45% of 120g
Find 34% of 350m
Find 12.5% of £150
Find 15% of £450
Find 9.75% of £420

15. Answers
45cm
48cm
54g
14m
£18.75
£67.50
£39.90

16. Ratio
Ratio is when you want to split something unevenly between several people
E.g. You have 10 sweets and 2 friends and yourself to share them with
You want the most and then your best friend gets the next most
You could split them 5 to you: 3 to your best friend: 2 to the other friend
The ratio is 5:3:2

17. Simplifying ratios
Ratios are really fractions and they need to be simplified
20:5
Both can be divided by 5 so it becomes
4:1
6:4:2?
All can be divided by 2
3:2:1

18. Try these Simplify these ratios; 10:5:20 5:5 7:7:14 12:6:6 9:3:6:3
24:16:8:80

19. Answers
2:1:4
1:1
1:1:2
2:1:1
3:1:2:1
3:2:1:10

20. Ratios with n
If you are asked to convert ratios into the form 1:n you must divide the first number down to 1 and divide the other side by this same number
E.g.
7:14
Both sides are divided by 7
So the answer is 1:2

21. Try these Convert these to the form 1:n 4:5 2:3 3:7.5 7:2 16:11
3:4
10:20

22. Answers
1:1.25
1:1.5
1:2.5
1:0.29
1:0.69
0.75:1
0.67:1
0.5:1

23. Using ratios If you want to split £21 in the ratio 2:1:4
How much does everybody get?
Ratios are like fractions so what do all these parts add up to?
2+1+4= 7
This means that they get 2/7:1/7:4/7
1/7 of £21 is £3
2/7 of £21 is £6
And 4/7 of £21 is £12
This is £6:£3:£12

24. Work out these £27 – 8:10 £3 – 4:4:2 £34 – 7:10 £4.40 – 2:8:10
70p – 18:9:3

25. Answers
£12 : £15
£1.20 : £1.20 : £0.60
£14 : £20
£0.44 : £1.76 : £2.20
42p : 21p : 7p