Arrange the following rational numbers in the ascending order 5 4 , 2 3 , 6 8 , 8 5 , 9 2 . Options: A . &nbsp 2 3 < 6 8 < 5 4 < 8 5 < 9 2 B . &nbsp 5 4 < 6 8 < 2 3 < 8 5 < 9 2 C . &nbsp 9 2 < 8 5 < 5 4 < 6 8 < 2 3 D . &nbsp 9 2 < 2 3 < 5 4 < 8 5 < 6 8

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 5 4 × 30 30 = 150 120 2 3 × 40 40 = 80 120 6 8 × 15 15 = 90 120 8 5 × 24 24 = 192 120 9 2 × 60 60 = 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 : 2 3 < 6 8 < 5 4 < 8 5 < 9 2

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

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 .

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

B .

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

C .

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

\frac{2}{3}

D .

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

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.