Question

Arrange the given fraction in ascending order.

$\frac{2}{15},\frac{12}{30},\frac{12}{45},\frac{3}{5}$

• A. $\frac{2}{15}<\frac{12}{30}<\frac{12}{45}<\frac{3}{5}$
• B. $\frac{2}{15}>\frac{12}{30}>\frac{12}{45}>\frac{3}{5}$
• C. $\frac{2}{15}<\frac{12}{45}<\frac{12}{30}<\frac{3}{5}$
• D. $\frac{2}{15}>\frac{12}{45}>\frac{12}{30}>\frac{3}{5}$

Answer 1

The correct option is C $\frac{2}{15}<\frac{12}{45}<\frac{12}{30}<\frac{3}{5}$

To compare the given fractions, the denominators of all the fractions need to be equal.
$\frac{2}{15}=\frac{2\times 1}{15\times 1}=\frac{2}{15}\frac{12}{45}=\frac{4\times 3}{15\times 3}=\frac{4}{15}\frac{12}{30}=\frac{6\times 2}{15\times 2}=\frac{6}{15}\frac{3}{5}=\frac{3\times 3}{5\times 3}=\frac{9}{15}$
So, we know when the denominator of all the fractions are equal, then the fractions can be simply compared based on the value of the numerator.

So, we can see that
$\frac{2}{15}<\frac{4}{15}<\frac{6}{15}<\frac{9}{15}$

Hence, our answer will be
$\frac{2}{15}<\frac{12}{45}<\frac{12}{30}<\frac{3}{5}$