Question

Multiply and reduce to lowest form and convert into a mixed fraction:$\left(\frac{11}{2}\right)\times \left(\frac{3}{10}\right)$

Answer 1

Step 1. Reduce $\left(\frac{11}{2}\right)\times \left(\frac{3}{10}\right)$ to the lowest form.

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

Reduce $\left(\frac{11}{2}\right)\times \left(\frac{3}{10}\right)$ to the lowest form:

$\begin{array}{rcl}\left(\frac{11}{2}\right)\times \left(\frac{3}{10}\right)& =& \frac{11\times 3}{2\times 10}\\ & \Rightarrow & \left(\frac{11}{2}\right)\times \left(\frac{3}{10}\right)=\frac{33}{20}\end{array}$

Since,$33$ and $20$ are co-prime i.e. they have no common factor other than one

Hence, $\frac{33}{20}$is in lowest form

Step 2. Convert $\frac{33}{20}$ into a mixed fraction.

A mixed fraction is a combination of a whole and a part that is obtained by dividing numerator with denominator,

such that $\frac{\mathrm{Dividend}}{\mathrm{Divisor}}=\mathrm{Quotient}\frac{\mathrm{Remainder}}{\mathrm{Divisor}}$ $\left[\because 20133-2013\right]$

Convert $\frac{33}{20}$ into a mixed fraction:

$\frac{33}{20}=1\frac{13}{20}$

Hence, the lowest form of $\left(\frac{11}{2}\right)\times \left(\frac{3}{10}\right)$ is $\frac{33}{20}$and its conversion into mixed fraction is $1\frac{13}{20}$.