Question

Which of the following is true for the fractions $\frac{1}{5}$ and $3\frac{2}{3}$ ?

• A. $3\frac{2}{3}$ < $\frac{1}{5}$
• B. $3\frac{2}{3}$ > $\frac{1}{5}$
• C. $3\frac{2}{3}$ = $\frac{1}{5}$
• D. $3\frac{2}{3}$ = $2\times \frac{1}{5}$

Answer 1

The correct option is B $3\frac{2}{3}$ > $\frac{1}{5}$

Converting the mixed fraction to an improper fraction, we have
$3\frac{2}{3}=\frac{(3\times 3)+\left(2\right)}{3}=\frac{11}{3}$

So, we are comparing $\frac{1}{5}$ and $\frac{11}{3}$.
For comparing two unlike fractions, we take the LCM of the denominators.
The LCM of 3 and 5 is 15.

Hence, we convert
$\frac{1}{5}\Rightarrow \frac{1\times 3}{5\times 3}=\frac{3}{15}$

$\frac{11}{3}\Rightarrow \frac{11\times 5}{3\times 5}=\frac{55}{15}$

Hence, $\frac{55}{15}>\frac{3}{15}$
$\Rightarrow$ $3\frac{2}{3}>\frac{1}{5}$.