**Fractions:**
Suppose you choose a Circle

Now In the above Circle, is divided into 6 parts and then it is shaded with 2 parts, so we say that fraction of the shaded part is 2 out of 6 that is $\frac{2}{6}$.

I think now you got an idea about fractions, Lets define a fraction

**Fraction:**
Fraction is of the form $\frac{Numerator}{denominator}$; here denominator is never equal to zero.

** **

Example: $\frac{3}{5}$, $\frac{9}{8}$

Example: $\frac{4}{0}$ cannot be a fraction since you can never select 4 items out of zero number of things.

Now we shall define Different types of fractions:

**1. **
**Proper Fraction**
: Here numerator is less than the denominator. Example $\frac{2}{5}$ that is 2 is less than 5.

**2. **
**Improper Fraction**
: Here numerator is greater than the denominator Example $\frac{5}{4}$ that is 5 is greater than 4.

**3. **
**Mixed fraction**
: An improper fraction converted to a whole number and a proper fraction is called a mixed fraction Example: 3$\frac{5}{6}$, 4$\frac{3}{2}$.

In this section we will try to do some operations on the Fractions.

**Addition of fractions:**

Consider two fractions $\frac{3}{4}$ and $\frac{5}{4}$

$\frac{3}{4}$ + $\frac{5}{4}$

Since they have common denominator we can add up the numerators freely like this

3 + $\frac{5}{4}$ = $\frac{8}{4}$ = 2.

**Subtraction of fractions:**

Consider two fractions $\frac{9}{4}$ and $\frac{1}{2}$ let us try to subtract it

$\frac{9}{4}$ - $\frac{1}{2}$ = 9$\frac{-1}{4}$ = $\frac{8}{4}$ = 2 [Here also we come across same denominator, so we can subtract freely the numerator and divide it by 4].

**Multiplication of fraction: **
Consider two fractions such as $\frac{2}{4}$ and $\frac{6}{8}$ now multiply these two

$\frac{2}{4}$ $\times$ $\frac{6}{8}$ = $\frac{12}{32}$ = $\frac{6}{16}$ = $\frac{3}{8}$ [you can simplify the answer by 2 table].

**Division of a fraction: **
Let us consider the above two fractions only and try to divide it

$\frac{\frac{2}{4}}{\frac{6}{8}}$. Here you need to invert the Denominator Like this

$\frac{2}{4} \times \frac{8}{6}$ then cancel 8 goes in 4, 2 times and 6 goes in 2, 3 times So our answer is $\frac{2}{3}$.

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