Question

Multiply the following fractions: $\frac{5}{6}\times 2\frac{3}{7}$

Answer 1

Step 1: Convert the given mixed fraction $2\frac{3}{7}$ into an improper fraction.

$\begin{array}{rcl}2\frac{3}{7}& =& \frac{\left(7\times 2\right)+3}{7}\\ & =& \frac{14+3}{7}\\ & =& \frac{17}{7}\end{array}$

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 $2\frac{3}{7}=\frac{17}{7}$ in the given expression and find the product of the two fractions:

$\begin{array}{rcl}\frac{5}{6}\times 2\frac{3}{7}& =& \frac{5}{6}\times \frac{17}{7}\\ & =& \frac{5\times 17}{6\times 7}\\ & =& \frac{85}{42}\end{array}$

Step 3: Convert the improper fraction $\frac{85}{42}$ into a mixed fraction.

Divide $85$ by$42$

$42285-\underline{8}\underline{4}1$

$\therefore \frac{85}{42}=2\frac{1}{42}$

Hence, $\frac{5}{6}\times 2\frac{3}{7}=2\frac{1}{42}$.