**Introduction :**

A fraction is a number that can represent part of a whole. The earliestfractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today.) and which consist of a numerator and a denominator, the numerator representing a number of equal parts and the denominator telling how many of those parts make up a whole.

**(**Source wikipedia)

Here we are going to know the types of fractions for solving and simplifying fractions in study guides

**Proper Fraction **- Numerator is lesser that denominator

**Improper Fraction** - Numerator is greater that denominator

**Mixed Fraction** - fraction with the whole number

**Equivalent Fraction** - denominator and numerator are multiplied by the same number

**Simplifying of Proper Fraction:**

**Example:**

`15/18 ` (divide both denominator and numerator by same number 3)

`5/6`

**Simplifying of Improper Fraction:**

**Example:**

`18/15` (divide both denominator and numerator by same number 3)

`6/5`

**Simplifying Mixed Fraction:**

**Example:**

`5 ` `1 /10` (multiply the whole number 5 by the denominator 10 and then add this product result with the numerator)

`((5 * 10) +1)/10`

`51/10`

**Simplifying Equivalent Fraction:**

Multiply or divide the both numerator and denominator. erator by the same number 2. So we get

`6/10 = (6 * 2)/ (10 * 2) = 12 / 20`

`6/10=(6-:2)/(10-:2)=3/5`

**Fractions for addition:**

**Example: `12/10 +13/10` **

If the denominators are same, we will do like belo

Fractions are added.`(12+13)/10` .

therefore the resultant fraction is `25/10` (divide both denominators and numerators by same number 5)

the result for the addition fraction is `5/2`

**Example:`12/10 +13/9` **

If the denominators are not same, we will find least common divisor. The lease common divisor for 10 and 9 is 90.

In `12/10` the denominator 10 is 9 times in the least common divisor. so we will multiply the numerator 12 by 9. 12 * 9 = 108.

In `13/9` ** **the denominator 9 is 10 times in the least common divisor. so we will multiply the numerator 13 by 10. 13 * 10 = 130

Now, we can add the denominator. so we will get `(108+130)/90= 238/90`

**Fractions for subtraction:**

**Example: `12/10-13/10` **

If the denominators are same, we will do like belo

Fractions are subtracted.`(12-13)/10`

therefore the resultant fraction is `-1/10`

**Example:`12/10-13/9` **

If the denominators are not same, we will find least common divisor. The lease common divisor for 10 and 9 is 90.

In `12/10 ` the denominator 10 is 9 times in the least common divisor. so we will multiply the numerator 12 by 9. 12 * 9 = 108.

In `13/9` ** **the denominator 9 is 10 times in the least common divisor. so we will multiply the numerator 13 by 10. 13 * 10 = 130

Now, we can add the denominator. so we will get `(108-130)/90= -22/90`

**Computing fractions for multiplication:**

`2/4* 4/3`

Here numerators are multiplied by numerators and denominators are multiplied by denominator and finally, simplified

`(2*4)/(4*3)`

`8/12 ` (divide both numerator and denominator by the same number 4)

`2/3`

Therefore the result for the multiplication fraction is `2/3`

**`4/3-:3/4` **

Firest we have to find reciprocal for the second fraction is `3/4` .Then we have to multiply this reciprocal with dividend fraction like below

`4/3 * 4/3`

Therefore the result is `16/9`