Question

Which of the following represent the smallest fraction?

• A. $\frac{1}{3}+\frac{1}{5}$
• B. $\frac{1}{3}÷\frac{1}{5}$
• C. $\frac{1}{3}-\frac{1}{5}$
• D. $\frac{1}{3}\times \frac{1}{5}$

Answer 1

The correct option is D

$\frac{1}{3}\times \frac{1}{5}$

Justification of answer:

Option (A):

$\frac{1}{3}+\frac{1}{5}$

Obtaining L.C.M of denominators of the above fractions, we get

L.C.M of $3$ and $5=15$

$\frac{1}{3}=\frac{1\times 5}{3\times 5}=\frac{5}{15}$

$\frac{1}{5}=\frac{1\times 3}{5\times 3}=\frac{3}{15}$

$\frac{1}{3}+\frac{1}{5}$$=\frac{5}{15}+\frac{3}{15}$

$=\frac{5+3}{15}$

⇒ $\frac{1}{3}+\frac{1}{5}$ $=\frac{8}{15}$

Option (B):

$\frac{1}{3}÷\frac{1}{5}$ $=$$\frac{1}{3}\times \frac{5}{1}$(reciprocal of the divisor is taken when multiplication replaces the division )

$=\frac{1\times 5}{3\times 1}$

⇒$\frac{1}{3}÷\frac{1}{5}$ $=$ $\frac{5}{3}$

Now $\frac{5}{3}$$=$$\frac{5\times 5}{3\times 5}$(converting into like fractions)

⇒ $\frac{5}{3}$$=$ $\frac{25}{15}$

Option C:

$\frac{1}{3}-\frac{1}{5}$

Obtaining L.C.M of denominators of the above fractions, we get

L.C.M of $3$ and $5=15$

$\frac{1}{3}=\frac{1\times 5}{3\times 5}=\frac{5}{15}$

$\frac{1}{5}=\frac{1\times 3}{5\times 3}=\frac{3}{15}$

$\frac{1}{3}-\frac{1}{5}$$=\frac{5}{15}-\frac{3}{15}$

$=\frac{5-3}{15}$

⇒ $\frac{1}{3}-\frac{1}{5}$ $=\frac{2}{15}$

Option D:

$\frac{1}{3}\times \frac{1}{5}$ $=\frac{1\times 1}{3\times 5}$

⇒$\frac{1}{3}\times \frac{1}{5}$ $=$$\frac{1}{15}$

Thus, on the basis of the above results, it is evident that option (D)$\frac{1}{15}$ is the smallest among all the fractions.