## Fractions

Fractions :-

A fraction is a number which represents a part of whole.

A fraction is written as
a / b   where a,b = whole numbers & b ≠ 0 , / =division line

a / b  =  N / D  =  Numerator / Denominator

Classification of Fractions :-

Note : here N=numerator, D=denominator
Type of Fractions Defination Example
Proper Fraction A fraction whose N is greater than 0 but less than its D 7/9, 2/5
Improper Fraction A fraction whose N >= D 8/3, 11/6
Mixed Fraction It consists of two parts, a natural number & a proper fraction. 3 2/7, 4 9/11
Decimal Fraction A fraction whose D = 10, 100, 1000 4/100, 2/10
Vulgar Fraction A fraction whose D = number other than 10,100,1000 5/11, 12/70
Like Fractions Two or more fractions having same D. 3/7, 11/7
Unlike Fractions two or more fractions having different D. 2/9, 3/5
Equivalent Fractions If two or more fractions have same value. 3/7 = 15/35
Simplest (irreducible) form of a Fraction (Lowest term) if N & D have no common factor (except 1). 3/7 is lowest term of 15/35

Note :- 1) Every natural number is an improper fraction.
2) Every mixed fraction is written as an improper fraction & vice-a-versa.

Basic Properties of Fractions :-

The value of a fraction does not change, if N & D of a fraction are
1) Multiplied by same ( non-zero ) number
2) Divided by same ( non-zero ) number.

Dividing the N & D by same number is called cancelling.

Conversion of given fractions to equivalent like fractions :-

1) Find LCM of denominator
2) Multiply each N & D of each fraction by such a number so that D of each fraction is LCM.

Comparison of Fractions :-

1) Convert all fractions into equivalent like fractions.
2) the fraction having the greater N is greater.
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