Comparision of fractions

Quote: The essence of mathematics is not to make simple things complicated, but to make complicated things simple.    --S.Gudder

Let me take one example
1. compare 1/4 and 3/4 
3/4 > 1/4

Rule 1 : If denominators of the both fractions are equal, compare numerators.

In the above example denominator of the both fractions is 4.
So compare 1 and 3.
As 3 > 1, 3/4 > 1/4

2. compare 3/7 and 3/9
 3/7 > 3/9

Rule 2 : if numerators of the both fractions are equal, denominator with more value is lesser.

 In the above example 3/7 and 3/9 having same numerator. So denominator with more value is lesser.
 In this case denominator 9 is more. So 3/9 is lesser than 3/7

3. compare 2/3 and 4/5 
    step 1 : 2/3   ?  4/5
    step 2 : 2x2/3x2 ? 4/5 ( multiply denominator and numerator with same value i.e. 2)
    Multiplying with 2 to make both the numerator will become same.

4. compare  2/7 and 5/9

    This is generic method and can be applied every example above. 

    Known as Cross multiplication method.

    step 1 : 2/7 , 5/9  ( cross multiplication : multiply numerator and denominator )

                2x9  ?  5x7

                18    ?  35

                18    <  35

          So  2/7 < 5/9

    In traditional method, need to find Least Common Multiple(L C M).
    LCM of 9 and 7 is 63 (9 x 7) as both are prime numbers. 

    So 2/7 x 9/9 and 5/9x7/7
          18/63 ? 35/63
          As denominators are equal 18/63 < 35/63 
          Hence 2/7 < 5/9

Lets look how to find LCM in next post...