Maths-
General
Easy

Question

8 Arrange the following rational numbers in ascending order fraction numerator 4 over denominator negative 5 end fraction comma fraction numerator negative 5 over denominator negative 12 end fraction comma fraction numerator 7 over denominator negative 18 end fraction and fraction numerator negative 2 over denominator 3 end fraction.

hintHint:

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

The correct answer is: Yes it's rational numbers


    Given rational numbers are fraction numerator 4 over denominator negative 5 end fraction comma fraction numerator negative 5 over denominator negative 12 end fraction comma fraction numerator 7 over denominator negative 18 end fraction and fraction numerator negative 2 over denominator 3 end fraction.
    Express the rational numbers with positive denominator by multiplying with -1.

    Here, fraction numerator 4 over denominator negative 5 end fraction equals fraction numerator 4 cross times negative 1 over denominator negative 5 cross times negative 1 end fraction equals fraction numerator negative 4 over denominator 5 end fraction and fraction numerator 7 over denominator negative 18 end fraction equals fraction numerator 7 cross times negative 1 over denominator negative 18 cross times negative 1 end fraction equals fraction numerator negative 7 over denominator 18 end fraction
    So, Now we have fraction numerator negative 4 over denominator 5 end fraction comma 5 over 12 comma fraction numerator negative 7 over denominator 18 end fraction and fraction numerator negative 2 over denominator 3 end fraction.
    By taking LCM of denominators 5,12,18 and 3, we get LCM as 180
    On multiplying fraction numerator negative 4 over denominator 5 end fraction with 36, we get fraction numerator negative 4 cross times 36 over denominator 5 cross times 36 end fraction equals fraction numerator negative 144 over denominator 180 end fraction
    On multiplying 5 over 12 with 15, we get fraction numerator 5 cross times 15 over denominator 12 cross times 15 end fraction equals 75 over 180
    On multiplying fraction numerator negative 7 over denominator 18 end fraction with 10, we get fraction numerator negative 7 cross times 10 over denominator 18 cross times 10 end fraction equals fraction numerator negative 70 over denominator 180 end fraction
    On multiplying fraction numerator negative 2 over denominator 3 end fraction with 60, we get fraction numerator negative 2 cross times 60 over denominator 3 cross times 60 end fraction equals fraction numerator negative 120 over denominator 180 end fraction
    On comparing the above fractions with same denominator,
    we have -144 < -120< -70 < 75
    Hence fraction numerator negative 144 over denominator 180 end fraction less than fraction numerator negative 120 over denominator 180 end fraction less than fraction numerator negative 70 over denominator 180 end fraction less than 75 over 180 equals fraction numerator negative 4 over denominator 5 end fraction less than fraction numerator negative 2 over denominator 3 end fraction less than fraction numerator negative 7 over denominator 18 end fraction less than 5 over 12
    So ascending order is fraction numerator 4 over denominator negative 5 end fraction comma fraction numerator negative 2 over denominator 3 end fraction comma fraction numerator 7 over denominator negative 18 end fraction comma 5 over 12

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