Question

Multiply and reduce to the lowest form and convert into a mixed fraction: $\left(\frac{5}{2}\right)\times 6$

Answer 1

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

Step 1: Multiply $\frac{5}{2}$ with $6$.

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,

$\left(\frac{5}{2}\right)\times 6=\frac{5\times 6}{2}=\frac{30}{2}$

Step 2: Reduce the improper fraction $\frac{30}{2}$ 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 lowest form of the improper fraction $\frac{30}{2}$ will be

$\frac{30÷2}{2÷2}=\frac{15}{1}=15$.

Hence, the multiplication of $\frac{5}{2}$ and $6$ reduced to the lowest form is equal to $15$ i.e., $\left(\frac{5}{2}\right)\times 6=15$.