What is fractions?
A fraction represents number of equal parts of a whole. This whole can be anything like distance, money, an object etc. It is a part or section of anything. Let’s take an example of a cake that you baked today. You want to share it to your mother and father. You have divided the cake into 4 equal parts and shared 1 part to your mummy and one part to your papa. kept 2 part to yourself. So, he/she has 2 part out of 4 or in other words 2 out of 4 parts. This can be written as 
. The number of equal parts is 4. It is the number of equal parts into which the cake has been divided. Here 4 is called denominator and 2 is called numerator.
Take another example as shown in the below figure 1.2. There is total 25 boxes and out of that 10 are shaded. Hence 10 out of 25 are shaded which can be written as 
or Now if you want to show fractions in a number line then how will you do it. Logic is same, divide the line in equal parts as per requirements. Suppose you need to show, then divide the line in 2 equal parts, for divide into 3 equal parts.
Types of Fractions
Proper Fractions – Numerator is always less than denominator. eg: 
Improper Fractions – Numerators are greater than denominator. eg: , etc.
Mixed Fractions – It is a combination of whole number and a proper fraction. Improper fractions are converted to mixed fraction by dividing the numerator by denominator. and is written as Quotient 
Example 1: = 3
Example 2: Express following mixed fractions as improper fractions:
Method 1
Figure 1.1: 
Method 2
Figure 1.2:
Figure 1.3: 
Like Fractions – They have same denominator. example 3 -. They can be compared by comparing their numerators.
Unlike Fractions – They have different denominators. Example 4 -, . To compare unlike fractions there are 2 methods.
By Finding LCM – Example: Compare 
and 
LCM of 3 and 4 is 12. Make the denominator as 12 by multiplying suitable.
number. So, 
= 
x 
= 
; 
= 
x
= 
Since 9>8, 
> 
or 
>
Step 1 – Find LCM of the denominator.
Step 2 – Express all the fractions with LCM as their denominator. This will convert unlike fractions into like fractions.
Step 3 – Compare the like fractions obtained in step 2.
Equivalent Fractions – When 2 or more fractions have same value on simplifying is called equivalent fraction. Example:,, are equivalent fractions and can be simplified by dividing numerator and denominator by same number. In other words, dividing numerator and denominator by their common factor. If you divide by highest common factor, then you will get simplest form.
Fact: A fraction is said to be in simplest form if its numerator and denominator have no common factor except 1.
Example 5:
Find 3 Equivalent fraction of 
Example 6: Find the equivalent fraction of 
with denominator 7.
We observe the denominator and nd 35รท5=7. We therefore divide both numerator and denominator by 5. Hence, 