Question

Evaluate the expression given below. $\frac{1}{3}\times \frac{1}{5}$ = ___

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

Answer 1

The correct option is D $\frac{1}{15}$

Detailed step-by-step solution:


In figure $A$, out of three, one column is shaded. This column’s length is one-third of the total length of one unit.
Length of one column = $\frac{1}{3}\text{unit}$

In figure $B$, one out of five rows is shaded. This row’s width is one-fifth of the total width of one unit.
Width of one row = $\frac{1}{5}\text{unit}$

After overlapping, the total number of sections formed is $15$. The number of overlapping sections is $1$.
Area of the whole figure = $1\text{unit}\times 1\text{unit}=1\text{sq unit}$

Area of one section = One-fifteenth of the total area = $1\text{sq unit}÷\frac{1}{5}=\frac{1}{15}\text{sq unit}$

Area of the overlapping sections = $\text{Area of one section}\times \text{Total number of overlapping sections}$

$=\frac{1}{15}\times 1=\frac{1}{15}\text{sq unit}$

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

Hence, option B is correct.