Question

Multiply and reduce to lowest form (if possible):$\left(\frac{2}{7}\right)\times \left(\frac{7}{9}\right)$.

Answer 1

The lowest form of a fraction

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

Reduce $\left(\frac{2}{7}\right)\times \left(\frac{7}{9}\right)$ into the lowest form:

$\begin{array}{rcl}\left(\frac{2}{7}\right)\times \left(\frac{7}{9}\right)& =& \frac{2\times 7}{7\times 9}\\ & \Rightarrow & \left(\frac{2}{7}\right)\times \left(\frac{7}{9}\right)=\frac{2}{9}\end{array}$

$2$ and $9$ are co-prime i.e. have no common factor other than one.

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