Question

Which of the following is the smallest?
$\frac{1}{4},\frac{1}{5},\frac{3}{4}$ and $\frac{2}{5}$

• A. $\frac{1}{4}$
• B. $\frac{1}{5}$
• C. $\frac{3}{4}$
• D. $\frac{2}{5}$

Answer 1

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

For comparing unlike fractions, we need to first convert them into like fractions.

$\frac{1\times 5}{4\times 5}=\frac{5}{20}$

$\frac{1\times 4}{5\times 4}=\frac{4}{20}$

$\frac{3\times 5}{4\times 5}=\frac{15}{20}$

$\frac{2\times 4}{5\times 4}=\frac{8}{20}$

Since $\frac{4}{20}<\frac{5}{20}<\frac{8}{20}<\frac{15}{20}$,

$\frac{1}{5}<\frac{1}{4}<\frac{2}{5}<\frac{3}{4}$

$\therefore \frac{1}{5}$ is the smallest.