1. Introduction to The Fractions

Fractions

A fraction is a number representing a part of a whole. It is written as    where a is the numerator and b is the denominator. 

Fraction as a Part of a Whole :   
If a birthday cake is divided into four equal parts, each part is represented as 1 part out of 4 equal parts and is written as 

The part that is considered (in this case, 1) is called the numerator. The number of parts into which the whole is divided (in this case, 4) is called the denominator.

is a fraction. We read it as “five-twelfths”. Here 12 stands for the number of equal parts into which the whole has been  divided and 5 stands for the number of equal parts which have been taken out.
Here 5 is called the numerator and 12 is called the denominator.

Ex.     What fraction of a day is 9 hours? 
Sol.     One day = 24 hours 

i.e.,     9 hours out of 24 hours. 

Fraction on the Number Line
In previous chapters we learnt to show whole numbers like 0,1,2... on a number line. We can also show fractions on a number line. Let us draw a number line and we try to mark 

is greater than 0 and less than 1, so it should lie between 0 and 1.

Since we have to show  we divide the gap between 0 and 1 into two equal parts and show 1 part as (As shown in figure)

Suppose we want to show on a number line. We divide the length between 0 and 1 into 3 equal partsand show one part as (as shown in the Figure)