Question

Arrange the following rational numbers in ascending order: $\frac{12}{16}$,$\frac{4}{9}$ and $\frac{6}{10}$

• A. $\frac{6}{10}$, $\frac{4}{9}$, $\frac{12}{16}$
• B. $\frac{4}{9}$, $\frac{6}{10}$, $\frac{12}{16}$
• C. $\frac{12}{16}$, $\frac{6}{10}$, $\frac{4}{9}$
• D. $\frac{12}{16}$, $\frac{4}{9}$, $\frac{6}{10}$

Answer 1

The correct option is B

$\frac{4}{9}$, $\frac{6}{10}$, $\frac{12}{16}$

To compare the fractions, make the denominators equal.

For that, we have to find LCM of denominators $16,9,10$

$16=2\times 2\times 2\times 2$

$9=3\times 3$

$10=2\times 5$

$\text{LCM of [16, 9, 10] =}$$2\times 2\times 2\times 2\times 3\times 3\times 5=720$

$\frac{12}{16}=\frac{12\times 45}{16\times 45}=\frac{540}{720}$

$\frac{4}{9}=\frac{4\times 80}{9\times 80}=\frac{320}{720}$

$\frac{6}{10}=\frac{6\times 72}{10\times 72}=\frac{432}{720}$

Comparing numerators, $\frac{320}{720}<\frac{432}{720}<\frac{540}{720}$

or $\frac{4}{9}<\frac{6}{10}<\frac{12}{16}$