Page 81 - ICSE Math 5
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Comparing Unlike Fractions

                    Unlike fractions with the same numerator

                    We can compare unlike fractions with the same numerator by comparing their denominators.

                    For example, look at the figures shown below.
                                                                                        1
                                                                                        2
                                                                                        1
                                                                                        3
                                                                                        1
                                                                                        4
                                                                                        1
                                                                                        5
                    1 1 1       1
                     ,  ,   and   are unlike fractions with the same numerator. On comparing their denominators,
                    2 3 4       5              1   1   1   1
                    we have 2 < 3 < 4 < 5. So,   >   >   >  .
                                               2   3   4   5
                    Thus, we can say that if two fractions have the same numerator and different denominators,
                    then the fraction with the smaller denominator represents the greater fraction and the fraction
                    with the greater denominator represents the smaller fraction.

                    Unlike fractions with different numerators

                    We can compare unlike fractions with different numerators by finding equivalent fractions using
                    the L.C.M. or cross-multiplication method.
                    L.C.M. Method

                    To compare unlike fractions with different numerators using L.C.M. method, we follow the given
                    steps.

                     •  Find the L.C.M. of the denominators of the given fractions.
                     •  Find an equivalent fraction of each given fraction with denominator equal to the L.C.M.
                     •  Compare the numerators of the fractions obtained in above step.

                    Cross-multiplication Method

                    To compare unlike fractions with different numerators using cross-multiplication method, we
                    do not find the L.C.M. of the denominators. Instead, we cross-multiply to compare the given
                    fractions.
                                            3      2
                    Example 9: Compare   and   using the L.C.M. method.
                                            4      5
                    Solution:     Step 1:  Find the L.C.M. of the denominators 4 and 5.                       2  4,  5

                                            L.C.M. of 4 and 5 = 2 × 2 × 5 = 20.                               2  2,  5
                                  Step 2:  Find an equivalent fraction of each fraction with                  5  1,  5
                                            denominator equal to the L.C.M.                                        1,  1
                                            3   3 × 5   15       2   2 × 4    8
                                              =        =    and   =         =
                                            4   4 × 5   20       5   5 × 4   20

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