Question

Evaluate the expression given below.
$\frac{2}{5}\times \frac{3}{7}$ = ___

• A. $\frac{6}{5}$
• B. $\frac{6}{35}$
• C. $\frac{6}{7}$
• D. $\frac{1}{35}$

Answer 1

The correct option is B $\frac{6}{35}$

Detailed step-by-step solution:


In figure $A$, two out of five columns are shaded. This column’s length is one-fifth of the total length of one unit.
Length of one column = $\frac{1}{5}\text{units}$; length of two columns $=\frac{2}{5}\text{units}$

In figure $B$, three out of seven rows are shaded. This row’s width is one-seventh of the total width of one unit.

Width of one row =$\frac{1}{7}\text{units}$; width of three rows =$\frac{3}{7}\text{units}$

After overlapping, the total number of sections formed is $35$. The number of overlapping sections is $6$.

Area of the whole figure = $1\text{unit}\times 1\text{unit}=1\text{sq. unit}$

Area of one section = One-thirty fifth of the total area =$1\text{sq unit}÷35=\frac{1}{35}\text{sq units}$

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

$=\frac{1}{35}\times 6=\frac{6}{35}\text{sq units}$

So, $\frac{2}{5}\times \frac{3}{7}=\frac{6}{35}$

Hence, option D is correct.