Maths-
General
Easy

Question

Which of the two rational numbers is greater in the given pair fraction numerator 9 over denominator negative 13 end fraction and fraction numerator 7 over denominator negative 12 end fraction

Hint:

Find the least common multiple of denominators.

The correct answer is: 9/-13


    Given rational numbers are fraction numerator 9 over denominator negative 13 end fraction and fraction numerator 7 over denominator negative 12 end fraction.
    Here, fraction numerator 9 over denominator negative 13 end fraction equals fraction numerator 9 x minus 1 over denominator negative 13 x minus 1 end fraction equals fraction numerator negative 9 over denominator 13 end fraction and fraction numerator 7 over denominator negative 12 end fraction equals fraction numerator 7 cross times negative 1 over denominator negative 12 cross times negative 1 end fraction equals fraction numerator negative 7 over denominator 12 end fraction
    So we have fraction numerator negative 9 over denominator 13 end fraction and fraction numerator negative 7 over denominator 12 end fraction
    By taking LCM of denominators 13 and 12, we get LCM as 156
    On multiplying fraction numerator negative 9 over denominator 13 end fraction with 12, we get fraction numerator negative 9 cross times 12 over denominator 13 cross times 12 end fraction equals fraction numerator negative 108 over denominator 156 end fraction
    On multiplying fraction numerator negative 7 over denominator 12 end fraction with 13, we get fraction numerator negative 7 cross times 13 over denominator 12 cross times 13 end fraction equals fraction numerator negative 91 over denominator 156 end fraction
    On comparing the above fractions with same denominator,
    we have -91 > -108
    Hence fraction numerator negative 91 over denominator 156 end fraction greater than fraction numerator negative 108 over denominator 156 end fraction equals fraction numerator 7 over denominator negative 12 end fraction greater than fraction numerator 9 over denominator negative 13 end fraction

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