How to add fractions with different denominators

In adding fractions with different denominators, find the least common multiple  of the fractions. That will then be the common denominator of the fractions. Then follow the steps of adding fractions with common denominator.

Examples:
1. 1/2 + 3/5         the denominator 2 and 5 are prime numbers so multiplying both equals to 10 as the
                             common denominator
                            following the least common multiple
                             2 = 2, 4, 6, 8, 10, 12,..........
                             5 = 10, 20, 30,.................        
                             with this multiples revealed that 10 is the least common multiple, therefore it will
                             then be the  common denominator of the fractions

   (1)(5)  + (3)(2)   =  To get  a denominator of 10, multiply (2)(5) in its denominator, multiply  also
   (2)(5)     (5)(2)         5 in its numerator so (1)(5) . Actually multiplying 5/5  to the fraction
                                    1/2 will just be renamed to 5/10 which is just same  as the                                
                                     original fraction 1/2 .
                                     In the fraction 3/5, multiply (3)(2) in its numerator and (5)(2) in its  
                                     denominator.
  5    +   6     =    11      adding both fraction with common denominator , the answer is 11/10
 10       10          10

2. 4/15 + 3/5                 the denominators are 15 and 5 ,getting the prime factors  provide us this table
                                      15 =      3 x  5
                                        5 = 1       x 5
                                               1 x 3 x 5 = 15   indicates as its  least common  denominator
                                     following the least common multiple
                                     15 = 15, 30, 45.......
                                       5=     5,   10,  15,  20, .....      LCM is 15     as the least common
                                                                                     denominator of the fractions
  4  +  (3)(3)  =
 15     (5)(3)                    4/15 is not changed because it holds the common denominator, so only 3/5
                                        is renamed as the denominator 5 multiplied by 3  will now be 15 .
 4    +   9      =    13          numerator must also be multiplied by 3  . multiplying a fraction of
15       15           15           3/3 is just equal to 1. So 3/5 =9/5.  The answer to the problem is 13/15





to be continued......
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