Question

Choose the correct descending order of the fractions $\frac{1}{5},\frac{3}{10}$ and $\frac{4}{15}:$

• A. $\frac{4}{15}>\frac{1}{5}>\frac{3}{10}$
• B. $\frac{1}{5}>\frac{4}{15}>\frac{3}{10}$
• C. $\frac{4}{15}>\frac{3}{10}>\frac{1}{5}$
• D. $\frac{3}{10}>\frac{4}{15}>\frac{1}{5}$

Answer 1

The correct option is D $\frac{3}{10}>\frac{4}{15}>\frac{1}{5}$

Let's compare $\frac{1}{5},\frac{3}{10}\text{and}\frac{4}{15}:$

Step 1: Find the LCM of denominators of the given fractions.
i.e. LCM of 5, 10 and 15:
5 can be written as $5:5\times 1$
10 can be written as $10:5\times 2$
15 can be written as $15:5\times 3$

Taking the factors with highest powers common, we get
$5^1\times 3^1$ from 15, $2^1$ from 10 and $1$ from 5.

Multiplying them, we get $5^1\times 3^1\times 2^1\times 1=30$ as the required LCM.

Step 2: Now, we multiply $\frac{1}{5},\frac{3}{10}$ and $\frac{4}{15}$ with $6,3$ and $2$ respectively to make their denominators as $30.$

$\therefore \frac{1}{5}=\frac{1\times 6}{5\times 6}=\frac{6}{30}$

$\frac{3}{10}=\frac{3\times 3}{10\times 3}=\frac{9}{30}$

and $\frac{4}{15}=\frac{4\times 2}{15\times 2}=\frac{8}{30}$

Step 3: When fractions have the same denominator, then the greatest fraction is the one with the greatest numerator.

So, just compare the numerators 6, 9 and 8.

Since $9>8>6$
$\therefore \frac{9}{30}>\frac{8}{30}>\frac{6}{30}$
$\Rightarrow \frac{3}{10}>\frac{4}{15}>\frac{1}{5}$