Question

Multiply and express as a mixed fraction:

$8\times 2\frac{2}{3}$

Answer 1

Step 1: Multiplying the given expression

$\begin{array}{rcl}8\times 2\frac{2}{3}& =& 8\times 2\frac{2}{3}\\ & =& 8\times \left(\frac{2\times 3+2}{3}\right)\\ & =& 8\times \left(\frac{6+2}{3}\right)\\ & =& 8\times \left(\frac{8}{3}\right)\\ & =& \frac{8\times 8}{3}\\ & =& \frac{64}{3}\end{array}$

Step 2: Converting into a mixed fraction

$\begin{array}{rcl}\frac{64}{3}& =& \frac{63+1}{3}\\ & =& \frac{63}{3}+\frac{1}{3}\\ & =& 21+\frac{1}{3}\\ & =& 21\frac{1}{3}\end{array}$

Hence, $8\times 2\frac{2}{3}=21\frac{1}{3}$