Question

Multiply and reduce to lowest form (if possible): $\left(\frac{3}{8}\right)\times \left(\frac{6}{4}\right)$.

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 $\left(\frac{3}{8}\right)\times \left(\frac{6}{4}\right)$ into the lowest form:

$$\begin{gathered} \begin{array}{rcl}\left(\frac{3}{8}\right)\times \left(\frac{6}{4}\right)& =& \frac{3\times 6}{8\times 4}\\ & \Rightarrow & \left(\frac{3}{8}\right)\times \left(\frac{6}{4}\right)=\frac{3\times 3}{4\times 4}\end{array} \\ \begin{array}{rcl}& \Rightarrow & \left(\frac{3}{8}\right)\times \left(\frac{6}{4}\right)=\frac{9}{16}\end{array} \end{gathered}$$

$3$ and $8$ are co-prime i.e. have no common factor other than one.

Hence $\frac{9}{16}$ is the lowest form of $\left(\frac{3}{8}\right)\times \left(\frac{6}{4}\right)$.