Question

Find the following product.

$\left(-\frac{1}{3}\right)\left(-7\frac{1}{2}\right)$

Short answer

The product is $\frac{5}{2}$.

Step-by-step solution

Step 1. Concept Used.

To multiply two fractions, simply multiply the numerators and denominators of both fractions together and then simplify further by cancel out any common factors.

Step 2. Simplify the mixed fraction.

First, simplify the mixed fraction into an improper fraction.

$\begin{array}{c}-7\frac{1}{2}=-\frac{7\times 2+1}{2}\\ =-\frac{14+1}{2}\\ =-\frac{15}{2}\end{array}$

Step 3. Find the product of given numbers.

Multiply the numerator and denominator and then simplify.

$$\begin{gathered} \left(-\frac{1}{3}\right)\left(-7\frac{1}{2}\right)=\left(-\frac{1}{3}·-\frac{15}{2}\right) \left[\mathrm{product}\mathrm{of}\mathrm{same}\mathrm{sign}\mathrm{is}\mathrm{positive}\right] \\ =\left(\frac{1}{3}·\frac{15}{2}\right) \\ =\frac{1·15}{3·2} \end{gathered}$$