Question

For the fractions $\frac{1}{3},\frac{1}{4}$ and $\frac{1}{5}$, which of the following order is true?

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

Answer 1

The correct option is C $\frac{1}{3}>\frac{1}{4}>\frac{1}{5}$

For comparing unlike fractions, we convert them into like fractions.
For this, we find the LCM of all the denominators, i.e, 3, 4 and 5.
$\therefore$ LCM of 3, 4 and 5 is 60.

Hence, we convert
$\frac{1}{3}\Rightarrow \frac{1\times 20}{3\times 20}=\frac{20}{60}$

$\frac{1}{4}\Rightarrow \frac{1\times 15}{4\times 15}=\frac{15}{60}$

$\frac{1}{5}\Rightarrow \frac{1\times 12}{5\times 12}=\frac{12}{60}$

Hence, $\frac{20}{60}>\frac{15}{60}>\frac{12}{60}$

Therefore, $\frac{1}{3}>\frac{1}{4}>\frac{1}{5}$ .