Question

Multiply and reduce to the lowest form and convert into a mixed fraction: $\left(\frac{2}{3}\right)\times 4$

Answer 1

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

Step 1: Multiply $\frac{2}{3}$ with $4$.

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,

$\left(\frac{2}{3}\right)\times 4=\frac{2\times 4}{3}=\frac{8}{3}$

Step 2: Reduce the improper fraction $\frac{8}{3}$ 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 $\frac{8}{3}$ will be $2\frac{2}{3}$.

Hence, the multiplication of $\frac{2}{3}$ and $4$ reduced and converted into a mixed fraction is equal to $2\frac{2}{3}$ i.e., $\left(\frac{2}{3}\right)\times 4=2\frac{2}{3}$.