CLASS-7
EQUIVALENT FRACTION

Equivalent Fraction

The value of a fraction remains the same if it’s numerator and denominator are multiplied or divided by the same number –

   X            a

------- = --------   ;  Xb = Ya  ,

   Y            b

    X                  a

--------  and  ---------   are equivalent  if  Xb = Ya  ,

    Y                  b

                      4           1

Example – 1  => ------- = -------  ;   8 = 8

                      8           2

 4/8 &  1/2 both are equivalent fraction

Example – 2 

                                      8            X

Find out the number ‘X’ where -------- = --------

                                     11           22

                 8  x  22

   =>  X  = ------------   =  16      

                    11

Simplest Form –

A fraction is said to be in the simplest form if its numerator & denominator have no factor in common except 1. It has been decided that, a fraction can be converted into its simplest form by cancelling out the common factors in the numerator and denominator. This can be done in two ways, 1) by prime factorization, 2) by HCF. 

1) Find the simplest form of fraction a 120 / 280

2)  If the HCF of 72 & 112  is 8 then find the simplest form.

           72         72 ÷ 8           9

Ans.)  ------- = ----------  = -------      (Ans.)

          112        112 ÷ 8          14