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                 \ 10-Nov-2025  Bharat Arora   Proof-8                                     Reader’s Sign _______________________ Date __________

                eqUAl FrACTionS

                Look at the following fractions for the shaded parts:

                The shaded part of each figure shows                        1                    1                     1
                       1  
                       
                half   . Are these halves equal?                          2                    2                     2
                       
                       2  
                Let us compare them.

                We can see that all the shaded parts are of
                different shapes and sizes. So, these are not equal.

                Now, consider the shaded parts of the following figures.

                Thus, equal fractions are parts of the same whole.

                eqUivAlenT FrACTionS

                Observe the fractions for the shaded parts.

                                            1                     2                     3                     4
                                            2                     4                     6                     8

                The shaded parts of all the figures are equal. Also, all the figures are of the same size.
                We notice that in each figure the shaded parts represent the same parts of the whole.

                So, the fractions represented by the shaded parts are also equal.
                        1    2    3    4
                Thus,   =      =    =
                        2    4    6    8
                Fractions that represent the same part of a whole are called equivalent fractions. The
                above fractions are equivalent fractions.

                Finding equivalent Fractions

                An equivalent fraction can be obtained by either multiplying or dividing the numerator

                and denominator of a fraction by the same non-zero number.

                                      × 2       × 2        × 2        × 2
                For example:      1    =    2    =     4    =    8    =    16
                                  2         4          8         16        32
                                      × 2       × 2        × 2        × 2

                       98        Mathematics 4

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