Question

Multiply and reduce to lowest form and convert into a mixed fraction: $13\times \frac{1}{3}$.

Answer 1

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

Step 1: Multiply $13$ with $\frac{1}{3}$.

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,

$\begin{array}{rcl}13\times \frac{1}{3}& =& \frac{13\times 1}{3}\\ & =& \frac{13}{3}\end{array}$

Step 2: Reduce the improper fraction $\frac{13}{3}$ 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 $\frac{13}{3}$ will be $4\frac{1}{3}$.

Hence, the multiplication of $13$ and $\frac{1}{3}$reduced and converted into a mixed fraction is equal to $4\frac{1}{3}$ i.e., $13\times \frac{1}{3}=4\frac{1}{3}$.