Fractions,+Decimanls+&+Percentages

=Fractions, Decimals and Percentages=

Fractions
A fraction can be described as 'a numerical quantity that is not a whole number', for example one half of a football match, a quarter of a metre, or one and three eighths of some cakes.

Fractions are generally written in the form of a numerator on top and denominator on the bottom.


 * Numerator:** How many parts of a whole are present
 * Denominator:** How many parts the whole has been divided into

Using the above definitions, the picture below would be written as: __3__ 4

This is because there are three slices of the pizza present, but to make a whole pizza you need four slices.

Decimals
The word 'Decimal' can be translated as 'based on 10' (from Latin //decima//). A 'Decimal Number' means there is a Decimal Point.

In a decimal, the number on the right hand side of the decimal point shows a part of a whole number. The first number after the decimal point shows 1/10ths of the whole number, the 2nd point shows 1/100ths of the whole number and the 3rd point shows 1/1000ths and so on.

For example, 4.2 can be translated as 4 and 2/10ths, whilst 5.31 would be equivalent to 5 and 31/100ths etc. Another example would be to think about money - there are 100 pence in £1, so 10p could be shown as £0.10, as it is 1/10th of a pound. 1p could be shown as £0.01. £4 and 37p would be shown as £4.37.

Percentages
The sign **%** stands for 'per cent' which means **'out of 100'**.

So:


 * 40% means 40 out of 100
 * 11% means 11 out of 100

Percents are used everywhere in real life, so pupils need to understand them well. =Converting between percentages and decimals=

To change a percentage to a decimal, **divide by 100**.Change 48% to a decimal: 48 ÷ 100 = 0.48 To change a decimal to a percentage, **multiply by 100**.Change 0.67 to a percentage: 0.67 x 100 = 67%

Fifteen percent is the same as the fraction 15/100 and the decimal 0.15. They all simply mean "fifteen out of a hundred." A percent can always be written as a decimal, and a decimal can be written as a percent, like this: 0.85 = 85%

=Converting between percentages and fractions= Write the percentage as a fraction over 100 and then simplify:

=Converting between percentages and fractions= Write the percentage as a fraction over 100 and then simplify:



=Percentage of a number= There are a number of ways to find a percentage of a given number:

To find 20% of 30, convert the 20% to a decimal and then multiply by 30.20% = 0.20.2 x 30 = 6 This is the best method as it always works.

Another way to find 20% of 30 is to first find 10% of 30 and t hen multiply by 2.10% of 30 is 30 ÷ 10 = 32 x 3 = 6

Or a third way would be to recognise that 20% is equivalent to one fifth, and so just divide 30 by 5.30 ÷ 5 = 6