Question

Your friend evaluates the expression. Is your friend correct? Explain your reasoning.

$\begin{array}{rcl}-\frac{2}{3}÷\frac{4}{5}& =& \frac{-3}{2}\times \frac{4}{5}\\ & =& \frac{-12}{10}\\ & =& -\frac{6}{5}\end{array}$

Answer 1

Step 1: Identify the mistake done by friend

Expression evaluated by friend

$\begin{array}{rcl}-\frac{2}{3}÷\frac{4}{5}& =& \frac{-3}{2}\times \frac{4}{5}\\ & =& \frac{-12}{10}\\ & =& -\frac{6}{5}\end{array}$

In Fraction division, the reciprocal of the second fraction is multiplied by the first fraction as $a÷b=a\times \frac{1}{b}$

But my friend had taken the reciprocal of first fraction, which is not correct.

Step 2: Correct explanation for evaluating the given expression

$\begin{array}{rcl}-\frac{2}{3}÷\frac{4}{5}& =& -\frac{2}{3}\times \frac{5}{4}\\ & =& -\frac{2\times 5}{3\times 4}\\ & =& -\frac{2\times 5}{3\times 2\times 2}\\ & =& -\frac{5}{3\times 2}\\ & =& -\frac{5}{6}\end{array}$

Thus, the value obtained by my friend for the expression $\begin{array}{rcl}& & -\frac{2}{3}÷\frac{4}{5}\end{array}$ is incorrect, the correct value is $-\frac{5}{6}$