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TET Syllabus - Mathematics Study Materials in Number System (Part VIII)

 

Teachers Eligibility Test - Paper 2

 

Class – VI Mathematics

 

                                       NUMBER SYSTEM

 

                                        FRACTIONS

Equivalent Fractions

 

Example: 1

Find three equivalent fractions of   .

Solution:

        Equivalent fractions of   is

      =  =

      =  = 

      =  = 

 

                       Comparison of Unlike Fractions

Example: 2

Sindhu ate  of the chocolate bar and Priya ate  of the chocolate bar. Who has eaten more?

Solution:

The portion of the chocolate eaten by Sindhu =

The portion of the chocolate eaten by Priya =

Here the portions of the chocolates eaten by both differ.

Finding the equivalent fractions of    and    .

Hence,

         =    = 

         =     = 

So,  >  .

Therefore, Sindhu has eaten more chocolates.

Example: 3

Arrange the fractions in ascending order:  ,  ,  .

Solution:

               Equivalent fractions of   are 

               Equivalent fractions of    are 

              Equivalent fractions of     are 

Therefore,  <  <

The ascending order of given fractions is  ,  .

                     Addition of unlike fractions:

Example: 4

Add   and   .

Solution:

         Given fractions are   and   .

These are unlike fractions.

The common multiple of 7 and 3 is 21.

Hence, we find the equivalent fractions of    and   with denominator 21.

      =     =  

     =     = 

  +    =   +

             = 

Hence,   +    =   .

                   Subtraction of unlike fractions:

Example: 5

Simplify  -  .

Solution:

   Common multiple of 2 and 3 is 6.

Equivalent fraction of    is  

      =  =

Equivalent fraction of    is  

 

      =   = 

 -   =    -   

         = 

Hence,  -   = 

Example: 6     

Find the difference between and   .

Solution:

         Given fractions are   and   .

These are unlike fractions.

So, let us convert them into 'like fractions' and compare.

The common multiple of 7 and 9 is 63.

Hence, we find the equivalent fractions of    and   with denominator 63.

Equivalent fraction of    is  

                =  =

Equivalent fraction of    is  

                   =   = 

                  -   =    -   

                            = 

                            = 

Hence, the difference between and    is     .

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