Q21. - Algebra 1

Question

Find the following product.

$-\frac{30}{11}·\left(-\frac{1}{3}\right)$

Step-by-Step Solution

Answer

The product is $\frac{10}{11}$.

Step 1. Concept Used.

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

Step 2. Find the product of given numbers.

First multiply the numerator and denominator.

$$\begin{gathered} -\frac{30}{11}·\left(-\frac{1}{3}\right)=\left(\frac{30}{11}·\frac{1}{3}\right) \left[\mathrm{product} \mathrm{of} \mathrm{same} s\mathrm{ign} \mathrm{is} \mathrm{positive}\right] \\ =\frac{30·1}{11·3} \\ =\frac{30}{33} \end{gathered}$$

Step 3. Evaluate the expression.

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

$$\begin{gathered} -\frac{30}{11}·\left(-\frac{1}{3}\right)=\frac{30}{33} \\ =\frac{3·10}{3·11} \left[\mathrm{divide} N \& D \mathrm{by} \mathrm{common} f\mathrm{actor} 3\right] \\ =\frac{\frac{3}{3}·10}{\frac{3}{3}·11} \\ =\frac{1·10}{1·11} \\ =\frac{10}{11} \end{gathered}$$