Maths-
General
Easy

Question

Arrange the numbers fraction numerator negative 3 over denominator 5 end fraction comma fraction numerator 7 over denominator negative 10 end fraction and fraction numerator negative 5 over denominator 8 end fraction in ascending order

Hint:

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

The correct answer is: ascending order


    Given rational numbers are fraction numerator negative 3 over denominator 5 end fraction comma fraction numerator 7 over denominator negative 10 end fraction and fraction numerator negative 5 over denominator 8 end fraction.
    Express the rational numbers with positive denominator by multiplying with -1.

    Here, fraction numerator 7 over denominator negative 10 end fraction equals fraction numerator 7 cross times negative 1 over denominator negative 10 cross times negative 1 end fraction equals fraction numerator negative 7 over denominator 10 end fraction
    So, Now we have fraction numerator negative 3 over denominator 5 end fraction comma fraction numerator negative 7 over denominator 10 end fraction and fraction numerator negative 5 over denominator 8 end fraction.
    By taking LCM of denominators 5,10 and 8, we get LCM as 40
    On multiplying fraction numerator negative 3 over denominator 5 end fraction with 8, we get fraction numerator negative 3 cross times 8 over denominator 5 cross times 8 end fraction equals fraction numerator negative 24 over denominator 40 end fraction
    On multiplying fraction numerator negative 7 over denominator 10 end fraction with 4, we get fraction numerator negative 7 cross times 4 over denominator 10 cross times 4 end fraction equals fraction numerator negative 28 over denominator 40 end fraction
    On multiplying fraction numerator negative 5 over denominator 8 end fraction with 5, we get fraction numerator negative 5 cross times 5 over denominator 8 cross times 5 end fraction equals fraction numerator negative 25 over denominator 40 end fraction
    On comparing the above fractions with same denominator,
    we have  -28 < -25 < -24
    Hence fraction numerator negative 28 over denominator 40 end fraction less than fraction numerator negative 25 over denominator 40 end fraction less than fraction numerator negative 24 over denominator 40 end fraction equals fraction numerator 7 over denominator negative 10 end fraction less than fraction numerator negative 5 over denominator 8 end fraction less than fraction numerator negative 3 over denominator 5 end fraction
    So ascending order is fraction numerator 7 over denominator negative 10 end fraction comma fraction numerator negative 5 over denominator 8 end fraction comma fraction numerator negative 3 over denominator 5 end fraction.

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