Question

Multiply and reduce to lowest form (if possible):$\left(\frac{2}{3}\right)\times 2\left(\frac{2}{3}\right)$.

Answer 1

Lowest form of fraction

A fraction is said to be in the lowest form if its numerator and denominator have no common factor other than one.

Reduce $\left(\frac{2}{3}\right)\times 2\left(\frac{2}{3}\right)$ into the lowest form:

$\begin{array}{rcl}\left(\frac{2}{3}\right)\times 2\left(\frac{2}{3}\right)& =& \frac{2}{3}\times \frac{8}{3}\\ & \Rightarrow & \left(\frac{2}{3}\right)\times 2\left(\frac{2}{3}\right)=\frac{2\times 8}{3\times 3}\\ & \Rightarrow & \left(\frac{2}{3}\right)\times 2\left(\frac{2}{3}\right)=\frac{16}{9}\end{array}$

$16$ and $9$ are co-prime i.e. have no common factor other than one.

Hence $\frac{16}{9}$ is the lowest form of $\left(\frac{2}{3}\right)\times 2\left(\frac{2}{3}\right)$.