Maths-
General
Easy

Question

Arrange the following rational numbers in descending order fraction numerator negative 5 over denominator 6 end fraction comma fraction numerator negative 7 over denominator 12 end fraction comma fraction numerator 13 over denominator negative 18 end fraction and fraction numerator 23 over denominator negative 24 end fraction.

Hint:

Find the least common multiple of denominators and then arrange in
descending order.

The correct answer is: Yes it's rational numbers


    Given rational numbers are fraction numerator negative 5 over denominator 6 end fraction comma fraction numerator negative 7 over denominator 12 end fraction comma fraction numerator 13 over denominator negative 18 end fraction and fraction numerator 23 over denominator negative 24 end fraction.
    Express the rational numbers with positive denominator by multiplying with.

    Here, fraction numerator 13 over denominator negative 18 end fraction equals fraction numerator 13 x minus 1 over denominator negative 18 x minus 1 end fraction equals fraction numerator negative 13 over denominator 18 end fraction and fraction numerator 23 over denominator negative 24 end fraction equals fraction numerator 23 x minus 1 over denominator negative 24 x minus 1 end fraction equals fraction numerator negative 23 over denominator 24 end fraction
    So, Now we have fraction numerator negative 5 over denominator 6 end fraction comma fraction numerator negative 7 over denominator 12 end fraction comma fraction numerator negative 13 over denominator 18 end fraction and fraction numerator negative 23 over denominator 24 end fraction.
    By taking LCM of denominators 6,12,18 and 24, we get LCM as 72
    On multiplying fraction numerator negative 5 over denominator 6 end fraction with 12, we get fraction numerator negative 5 cross times 12 over denominator 6 cross times 12 end fraction equals fraction numerator negative 60 over denominator 72 end fraction
    On multiplying fraction numerator negative 7 over denominator 12 end fraction with 6, we get fraction numerator negative 7 cross times 6 over denominator 12 cross times 6 end fraction equals fraction numerator negative 42 over denominator 72 end fraction
    On multiplying fraction numerator negative 13 over denominator 18 end fraction with 4, we get fraction numerator negative 13 cross times 4 over denominator 18 cross times 4 end fraction equals fraction numerator negative 52 over denominator 72 end fraction
    On multiplying fraction numerator negative 23 over denominator 24 end fraction with 3, we get fraction numerator negative 23 cross times 3 over denominator 24 cross times 3 end fraction equals fraction numerator negative 69 over denominator 72 end fraction
    On comparing the above fractions with same denominator,
    we have  -42 > -52 > -60 > -69
    Hence fraction numerator negative 42 over denominator 72 end fraction greater than fraction numerator negative 52 over denominator 72 end fraction greater than fraction numerator negative 60 over denominator 72 end fraction greater than fraction numerator negative 69 over denominator 72 end fraction equals fraction numerator negative 7 over denominator 12 end fraction greater than fraction numerator 13 over denominator negative 18 end fraction greater than fraction numerator negative 5 over denominator 6 end fraction greater than fraction numerator 23 over denominator negative 24 end fraction
    So descending order is fraction numerator negative 7 over denominator 12 end fraction comma fraction numerator 13 over denominator negative 18 end fraction comma fraction numerator negative 5 over denominator 6 end fraction comma fraction numerator 23 over denominator negative 24 end fraction

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