Question

Multiply the following fractions: $6\frac{2}{5}\times \frac{7}{9}$

Answer 1

Step 1: Convert the given mixed fraction $6\frac{2}{5}$ into an improper fraction.

$\begin{array}{rcl}6\frac{2}{5}& =& \frac{\left(5\times 6\right)+2}{5}\\ & =& \frac{30+2}{5}\\ & =& \frac{32}{5}\end{array}$

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 $6\frac{2}{5}=\frac{32}{5}$ in the given expression and find the product of the two fractions:

$\begin{array}{rcl}6\frac{2}{5}\times \frac{7}{9}& =& \frac{32}{5}\times \frac{7}{9}\\ & =& \frac{32\times 7}{5\times 9}\\ & =& \frac{224}{45}\end{array}$

Step 3: Convert the improper fraction $\frac{224}{45}$ into a mixed fraction.

Divide $224$by $45$

$454224-\underline{1}\underline{8}\underline{0}44$

$\therefore \frac{224}{45}=4\frac{44}{45}$

Hence, $6\frac{2}{5}\times \frac{7}{9}=4\frac{44}{45}$.