Question

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

• A. 6/10, 4/9, 12/16
• B. 4/9, 6/10, 12/16
• C. 12/16, 6/10, 4/9
• D. 12/16, 4/9, 6/10

Answer 1

The correct option is B

4/9, 6/10, 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, $\frac{320}{720}<\frac{432}{720}<\frac{540}{720}$
$\therefore \frac{4}{9}<\frac{6}{10}<\frac{12}{16}$