Question

Find the following product.

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

Short answer

The product is $-\frac{1}{2}$.

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. Find the product of given numbers.

First, multiply the numerator and denominator.

$$\begin{gathered} \frac{3}{2}·\left(-\frac{1}{3}\right)=-\left(\frac{3}{2}·\frac{1}{3}\right) \left[\mathrm{productofdifferentsignisnegative}\right] \\ =-\left(\frac{3·1}{2·3}\right) \\ =-\left(\frac{3}{6}\right) \end{gathered}$$

Step 3. Evaluate the expression.

Write numerator and denominator in factored form and then cancel out the common factor.

$$\begin{gathered} \frac{3}{2}·\left(-\frac{1}{3}\right)=-\left(\frac{3}{6}\right) \\ =-\left(\frac{3}{3·2}\right) \left[\mathrm{divideN}\&\mathrm{Dbycommonfactor}3\right] \\ =-\left(\frac{\frac{3}{3}}{\frac{3}{3}·2}\right) \\ =-\left(\frac{1}{1·2}\right) \\ =-\left(\frac{1}{2}\right) \end{gathered}$$