Question

Multiply the following fractions: $3\frac{4}{7}\times \frac{3}{5}$

Answer 1

Step 1: Convert the given mixed fraction $3\frac{4}{7}$ into an improper fraction.

$\begin{array}{rcl}3\frac{4}{7}& =& \frac{\left(7\times 3\right)+4}{7}\\ & =& \frac{21+4}{7}\\ & =& \frac{25}{7}\end{array}$

Step 2: Multiply the two fractions.

We know that, according to the rule of multiplication of two fractions:

$\mathrm{Product}\mathrm{of}\mathrm{two}\mathrm{fractions}=\frac{\mathrm{Product}\mathrm{of}\mathrm{Numerators}}{\mathrm{Product}\mathrm{of}\mathrm{Denominators}}$

Substitute $3\frac{4}{7}=\frac{25}{7}$ in the given expression and find the product of the two fractions:

$\begin{array}{rcl}3\frac{4}{7}\times \frac{3}{5}& =& \frac{25}{7}\times \frac{3}{5}\\ & =& \frac{25\times 3}{7\times 5}\\ & =& \frac{5\times 3}{7\times 1}\\ & =& \frac{15}{7}\end{array}$

Step 3: Convert the improper fraction $\frac{15}{7}$ into a mixed fraction.

Divide $15$ by $7$

$7215-\underline{1}\underline{4}1$

$\therefore \frac{15}{7}=2\frac{1}{7}$

Hence, $3\frac{4}{7}\times \frac{3}{5}=2\frac{1}{7}$.