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EQUIVALENT FRACTIONS
        (ii)   5  =   5 × 2  =   5 × 3   =   5 × 4   =    5 × 5
               7      7 × 2      7 × 3       7 × 4        7 × 5
 Look at the figures given below.
                     5  =  10   =  15  =   20  =  25

 1                   7     14      21      21     35
 2             Hence, the four fractions equivalent to   5  are  10  ,  15  ,  20  and  25
 2                                                     7       14     21      21        35
 4             5       8 × 2      8 × 3       8 × 4        8 × 5
 3      (iii)   11  =  11 × 2  =  11 × 3  =   11 × 4  =   11 × 5
 6                   5      16     24      32      40
 4                   11  =  22  =  33   =  44  =   55

 8                                                    8        16     24      32        40
 Clearly, the shaded portions of these figures are equal.     Hence, the four fractions equivalent to    are  ,  ,  and
 1  2  3  4                                           11       22     33      44        55
 =  =  =  =
 2  4  6  8                                               3
        EXAMPLE 2:            Write afraction equivalent to     with numerator 15.
 These fractions are called equivalent fractions.  3  15  4
        SOLUTION:             Let       =
 1  1 × 2  1 × 3  1 × 4            4
 Note that   =  =  =
 2  2 × 2  2 × 3  2 × 4           Clearly, 15 = (3 × 5).

                              So, we multiply the denominator also by 5.
 It shows that multiplying the numerator and the denominator of a fraction by the same nonzero number does not   3  3 × 5  15
 change the value of the fraction.   =           =
 Similarly, dividing the numerator and the denominator of a fraction by the same nonzero number does not        4  4 × 5  20
 change the value of the fraction.                           15
 All such fractions are known as equivalent fractions.           Hence, the required fraction is    20  •
                                                          5
 EQUIVALENT FRACTIONS Two or more fractions representing the same part of a whole are called   EXAMPLE 3:    Write ajraction equivalent to     with denominator 56.
                                                          8
 equivalentfractions.                     5
        SOLUTION:                    Let       =
                                          8       56
 RULE:To get afraction equivalent to a givenfraction, we multiply or divide the numerator and the denominator            Clearly, 56 = (8 × 7).
 of the given fraction by the same nonzero number.
                              So, we multiply the numerator also by 7.

 SOLVED EXAMPLES                   5  =   5 × 7   =    35
                                  8       8 × 7        56
 EXAMPLE 1.    Write four fractions equivalent to each of the following.  35

 3  5  8                      Hence, the required fraction is      •
 (a)  (b)  (c)                                               56
 4  7  11                                                 36

 SOLUTION:    3  =  3 × 2  =  3 × 3  =  3 × 4  =  3 × 5  EXAMPLE 4:    Write fraction equivalent to    63   with numerator 4.
 4  4 × 2  4 × 3  4 × 4  4 × 5     36        4

 3  =  6  =  9  =  12  =  15  SOLTUION:   Let  63  =
   4  8  12  16  20        Clearly, 4 = 36 ÷ 9.


          Hence, the four fractions equivalent to are   3  ,  6  ,  9  ,  12  and  15        So, we divide the denominator also by 9.
 4  8  12  16  20
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