Question

Arrange the following rational numbers in the ascending order
$\frac{5}{4},\frac{2}{3},\frac{6}{8},\frac{8}{5},\frac{9}{2}.$

• 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 1

The correct option is A

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

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