APPLICATION OF NUMBER LEVEL 2

FRACTIONS, DECIMALS AND PERCENTAGES

After completing this unit, you will be able to:

· Convert between fractions, decimals and percentages

· Evaluate one number as a fraction or percentage of another

FRACTIONS

A fraction is a way of expressing a part of a whole. In the fraction 3/4, the number on the top, 3,

is called the numerator, the number on the bottom, 4, is called the denominator.

If the numerator is bigger than the denominator, the fraction is improper and is greater than one whole,

for example 8/5.

DECIMALS

A decimal is another way of expressing a part of a whole. In the decimal number 0.35741

The 3 stands for 3/10

The 5 stands for 5/10

The 7 stands for 7/1000 etc

PERCENTAGES

A percentage is another way of expressing part of one whole. Per cent means per 100, so 30% is 30/100.

CONVERTING FROM FRACTIONS TO DECIMALS

To convert a fraction to a percentage we:

“divide the numerator by the denominator”

Examples

1. Convert 3/4 to a decimal.

Solution

The fraction 3/4 literally means. ¾.

To change 3/4 to a decimal we divide 3 by 4 to get 0.75

2. Convert 1/3 to a decimal.

Solution

1/3 gives 0.3333333…. This is an example of a recurring decimal.

It can be written as 0.3.

CONVERING FROM DECIMALS TO FRACTIONS

Examples

1. Convert 0.23 to a fraction.

Solution

We know that the 2 stands for 2/10, and the 3 stands for 3/100.

So 0.23 as a fraction would be 23/100.

2. Convert 0.125 to a fraction.

Solution

0.125 can be written as 125/1000.

We are normally expected to write fractions in their lowest terms.

This means that we look for a common factor in the numerator and the denominator. In this case 125/1000 can be cancelled down and written as an equivalent fraction.

125/1000 = 5/40 dividing top and bottom by 25

5/40 = 1/8 dividing top and bottom by 8

CONVERTING FRACTIONS AND DECIMALS TO PERCENTAGES

To convert a fraction or a decimal to a percentage we:

“multiply by 100”

Examples

1. Convert 5/8 to a percentage.

Solution

We need to work out 5/8 x 100.

In the exam you can not use a calculator. You need to be able to work out such calculations by looking for a common factor and cancelling down.

We first write the calculation as 5/8 x 100/1.

We can see that 4 is a common factor. Cancelling down gives:

Answer =

5/2 x25/1 = 125/2 = 62.5 %

2. Convert 0.462 to a percentage.

Solution

We need to work out 0.462 x 100.

Remember multiplying by 100 means moving the decimal point two places to the right.

Answer =

0.462 x 100 = 46.2 %

CONVERTING PERCENTAGES TO FRACTIONS AND DECIMALS

To convert percentages to fractions and decimals we:

“divide by 100”

Examples

1. Convert 65% to a fraction.

Solution

65% = 65/10.

Remember to give the fraction in its lowest terms. 5 is a common factor.

65/100 = 13/20

2. Convert 2.5% to a decimal.

Solution

2.5 % = 25/100

Remember when we divide by 100 we move the decimal point two places to the left.

2.5/100 = 0.025

THE FOLLOWING EQUIVALENCES BETWEEN FRACTIONS DECIMALS AND PERCENTAGES ARE WORTH REMEMBERING

FRACTION	DECIMAL	PERCENTAGE
1/10	0.1	10%
1/4	0.25	25%
1/3	0.3	33.3 or 33 1/3%
1/2	0.5	50%
2/3	0.6	66.6% or 66 2/3%
3/4	0.75	75%

EXPRESSING ONE NUMBER AS A FRACTION OR A PERCENTAGE OF ANOTHER

· To express a number as a fraction of another number we write:

First number/second number and express in its lowest terms.

Examples

1. Express 8 as a fraction of 12.

Solution

8/12 = 2/3

3. Express 60 gms as a fraction of 1 kg.

Solution

In order to express one quantity as a fraction of another we must write them in the same units.

As 1 kg = 1,000 gms, we write:

60/1000 = 6/100 = 3/50

· To express a number as a percentage of another number we write:

Firstnumber/second number x 100

Examples

1. Express 16 as a percentage of 80.

Solution

16/8 x 100/1 = 16/4 x 5/1 dividing top and bottom by 20

Answer = 20%

16/4 x 5/1 = 4x5 =20

2. Express 55p as a percentage of £11.

Solution

In order to express one quantity as a percentage of another we must write them in the same units.

£11 = 1100p

Answer = 5%

55/1100 x100/1 = 5/100 x 100/1 = 5%