Arrange the following rational numbers in the ascending order 54,23,68,85,92.

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Question

Arrange the following rational numbers in the ascending order

\frac{5}{4}, \frac{2}{3}, \frac{6}{8}, \frac{8}{5}, \frac{9}{2} .

Options:

A . 23

B . 54

C . 92

D . 92

Answer: Option A
:
A
To compare the rational numbers, we first make the denominators equal.
L.C.M of the denominators 4, 3, 8, 5, 2 is 120.
Equivalent fractions with the denominator 120 are

\frac{5}{4} \times \frac{30}{30} = \frac{150}{120}

\frac{2}{3} \times \frac{40}{40} = \frac{80}{120}

\frac{6}{8} \times \frac{15}{15} = \frac{90}{120}

\frac{8}{5} \times \frac{24}{24} = \frac{192}{120}

\frac{9}{2} \times \frac{60}{60} = \frac{540}{120}

Since the denominator is same in the above equivalent fractions, we can decide the ascending order based on the numerator values.
Ascending order :

\frac{2}{3} < \frac{6}{8} < \frac{5}{4} < \frac{8}{5} < \frac{9}{2}

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