Question

Multiply and reduce to lowest form and convert into a mixed fraction: $11\times \frac{4}{7}$.

Answer 1

Reduce the product to the lowest form and convert into a mixed fraction.

Step 1: Multiply $11$ with $\frac{4}{7}$.

Multiplication of a fraction by a whole number.

“To multiply a whole number with a proper or an improper fraction, we multiply the whole number with the numerator of the fraction, keeping the denominator same.”

Therefore,

$\begin{array}{rcl}11\times \frac{4}{7}& =& \frac{11\times 4}{7}\\ & =& \frac{44}{7}\end{array}$

Step 2: Reduce the improper fraction $\begin{array}{rcl}& & \frac{44}{7}\end{array}$ to the lowest form and convert it into a mixed fraction.

Define the lowest form of a fraction.

A fraction is said to be in the simplest (or lowest) form if its numerator and denominator have no common factor except $1$. For example, the lowest form of the fraction $\frac{36}{54}$ is $\frac{36}{54}=\frac{36÷18}{54÷18}=\frac{2}{3}$

Define mixed fraction.

A mixed fraction has a combination of a whole and a part. For example, $7\frac{2}{3}$ is a mixed fraction.

Convert an improper fraction into a mixed fraction.

We can express an improper fraction as a mixed fraction by dividing the numerator by the denominator to obtain the quotient and the remainder. Then the mixed fraction will be written as $\mathrm{Quotient}\frac{\mathrm{Remainder}}{\mathrm{Divisor}}$.

Therefore, the mixed fraction of the improper fraction $\frac{44}{7}$ will be $6\frac{2}{7}$.

Hence, the multiplication of $11$ and $\frac{4}{7}$ reduced and converted into a mixed fraction is equal to $6\frac{2}{7}$ i.e., $11\times \frac{4}{7}=6\frac{2}{7}$.