All Kinds of Fractions

A fraction means a part of a whole group or its region.A fraction written as  number  with the bottom part (denominator) showing how many parts the whole is divided into, and the top part (numerator). Fraction in all kinds can be written as many types which depends upon the numerator and denominator by its value.
Fraction in all kinds are

Proper fractions
Improper fractions
Mixed fractions

I like to share this Converting Fractions with you all through my article.

Classification for all kinds of Fractions:

Proper Fractions:
proper fraction is explained as  the denominator shows the number of parts into which whole divided and the numerator expressed  the number of parts which  we taken out. In other words numerator less than denominator.

Example:
`3/10,2/5`
Improper Fractions:
Improper fractions is the fraction whose  numerator is greater  than the denominator are called improper fractions.

Example:
`7/2, 9/7`

Mixed Fractions:
A  mixed fraction is typical fraction which  has  combination of a whole and its part.

Example:
2` 3/4,` 7` 2/9` ,



Addition and Subtraction fractions in all kinds:

Procedure for addition:

For addition,fraction numbers with same denominator, denominator remain same number and we add only the numerator.
For addition with different denominator fraction  we have to take lcm for all denominator and convert different denominator  into like denominator by taking LCM and add.


Example 1:
Add `1/5` and  `3/5`

Solution :
In this proper fraction we have same denominator
`1/5 +3/5` =` (1+3)/5`

=`4/5`
Example 2:

Add `2/3` and `1/5`
Solution:
In this fraction we have different denominator  so,we take LCM
The LCM of 3 and 5 is 15.

Therefore,`2/3+1/5` =`(2xx5)/(3xx5)+(1xx3)/(5xx3)`

=`10/15+3/15`

=`13/15`

Example 3:
Add `1 4/5` and `3 5/6`

Solution:
`1 4/5 +3 5/6` =  `(5+4)/5+(18+5)/6`


Now `9/5+23/6` =`(9xx6)/(5xx6)+(23xx5)/(6xx5) `    since LCM of 5,6 =30

=`36/30+115/30`

=`151/30`

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Rules for subtraction:

For subtraction,fraction numbers with same denominator, denominator remain same number and we subtract only the numerator.



For subtraction with different denominator fraction  we have to take lcm for all denominator and convert different denominator  into like denominator by taking LCM and subtract.


Example 1:

subtract  `1/3` from `2/3`
Solution:
here same denominator
`2/3-1/3`    =`(2-1)/3`

Example 2:
Find fraction for `4 2/5-2 1/3`

Solution :
Taking LCM for 5 and 3 is 15 because of different denominator
`4 2/5 -2 1/3` =  `22/5-7/5`
= `(22xx3)/(5xx3) -(7xx5)/(3xx5)`

=`66/15 -35/15`

=`(66-35)/15`

=`31/15`