Mathematics GCSE - Unit 1 Statitics and Probabilitly

These 3 are 3 different ways of expressing a Proportion of something.

To convert one of these proportions to another is simple as you:

Divide you fraction top from bottom e.g. 1/2 = 1 divided by 2 = 0.5 to a decimal

Times the decimal by 100 will make the percentage e.g. 0.5 x 100 = 50%

The opposite way to do this is:

divide the percentage by 100 to get the decimal e.g. 50% divided by 100 = 0.5 to a decimal

To convert a decimal to a fraction, look at these examples to get the pattern:

Decimal

Fraction

0.6

6/10

0.12

12/100

0.345

345/1000

0.3

3/10

0.78

78/100

0.908

908/1000

0.7

7/10

0.45

45/100

0.024

24/1000

0.x .......... 0.xy ..........  0.xys

x/10 .......... xy/100 .......... xyz/1000

0.05

5/100

Examples:

Fraction

Decimal

Percentage

1/2

0.5

50%

1/4

0.25

25%

3/4

0.75

75%

1/3

0.33333333...

33%

2/3

0.66666666...

67%

1/10

0.1

10%

2/10

0.2

20%

X/10

0.X

X0%

1/5

0.2

20%

2/5

0.4

40%

There are 3 different types of using percentages:

Type 1

Find x% of y

e.g. Find 15% of £46

0.15 x 46 = £6.90

Type 2

Express x as a percentage of y

 e.g. Give 40p as a percentage of £3.34

(40 divided by 334) x 100 = 12%

Type 3

Find the new value when y decrease by x%

e.g. A shirt is on sale for 20% off the original price. If the original price was £30, how much is it in the sale?

A decrease of 20% means you have to multiply by 1 - 0.2 = 8 

30 x 0.8 = £24