Fast way to calculate FractionI want to solve this problem not by using common denominator. Is there any innovative and fast way ?. 1 6 + 4 21 + 5 84 + 7 228 + 9 532 = ?

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Fast way to calculate FractionI want to solve this problem not by using common denominator. Is there any innovative and fast way ?.            1      6        +            4      21        +            5      84        +            7      228        +            9      532        =               ?

knolsaadme · Accepted Answer

You can avoid converting to the single common denominator   1596 here by grouping terms in a way that creates some nice cancellations:                                          1            6                          +                              4            21                          +                              5            84                          +                              7            228                          +                              9            532                                              =                              1            6                          +                  (                                    4              21                                +                                    5                              4                ⋅                21                                              )                +                  (                                    7                              3                ⋅                76                                              +                                    9                              7                ⋅                76                                              )                                                  =                              1            6                          +                                            16              +              5                                      4              ⋅              21                                      +                                            49              +              27                                      21              ⋅              76                                                                        =                              1            6                          +                              21                          4              ⋅              21                                      +                              76                          21              ⋅              76                                                                        =                              1            6                          +                              1            4                          +                              1            21                              From here it&#039;s fairly easy to get            1      6        +            1      4        +            1      21        =            5              4        ⋅        3              +            1              7        ⋅        3              =                    35        +        4                    28        ⋅        3              =            13      28      Whether this is innovative or fast is hard to say. But I think it beats computing                    1        ⋅        266        +        4        ⋅        76        +        5        ⋅        19        +        7        ⋅        3        +        9        ⋅        7                    3        ⋅        4        ⋅        7        ⋅        19

Fast way to calculate Fraction I want to solve this problem not by using common denominator. Is the

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