Question

Multiply and reduce to the lowest form and convert into a mixed fraction: $2\times \left(\frac{6}{7}\right)$

Answer 1

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

Step 1: Multiply $2$ with $\frac{6}{7}$.

“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,

$2\times \left(\frac{6}{7}\right)=\frac{2\times 6}{7}=\frac{12}{7}$

Step 2: Reduce the improper fraction $\frac{12}{7}$ to the lowest form and convert it into a mixed 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 $\frac{36}{54}=\frac{36÷18}{54÷18}=\frac{2}{3}$

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

Therefore, the mixed fraction of the improper fraction $\frac{12}{7}$ will be $1\frac{5}{7}$.

Hence, the multiplication of $2$ and $\frac{6}{7}$ reduced and converted into a mixed fraction is equal to $1\frac{5}{7}$ i.e., $2\times \left(\frac{6}{7}\right)=1\frac{5}{7}$.