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)

 

Chapter 7

Fractions

Introduction to The Fractions

A fraction is a number representing a part of a whole. The total may be a single object or a group of objects. The other way round, we can say that a fraction is an operation on a number.
A Fraction
A fraction means a part of a group or of a region. 34 is a fraction. We read it as “ Three- fourths ”.

The first one is the whole i.e. a complete circle.
In the alternate circle, if we divide the circle into two equal corridor then the shadowed portion is the half i.e. ½ of the circle.
In the third circle, if we divide the circle into four equal corridor and shade only one part then the shadowed part is the one fourth i.e. ¼ of the whole circle.
In the fourth circle, if we divide the circle into four equal corridor and shade three corridor then the shadowed part is the three fourth i.e. ¾ of the whole circle.


Then, four stages for the number of equal region into which the total has been divided and three stages for the number of equal region, which have been taken out.