Q24. - Algebra 1

Question

Find the following product.

$\frac{2}{7}·4\frac{2}{3}$

Step-by-Step Solution

Answer

The product is $\frac{4}{3}$.

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, simplify the mixed fraction into an improper fraction and then simplify the product.

$$\begin{gathered} 4\frac{2}{3}=\frac{4\times 3+2}{3} \\ =\frac{14}{3} \\ \left(\frac{2}{7}\right)·\left(4\frac{2}{3}\right)=\left(\frac{2}{7}·\frac{14}{3}\right) \\ =\frac{28}{21} \end{gathered}$$

Step 3. Evaluate the expression.

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

$$\begin{gathered} \frac{2}{7}·\left(4\frac{2}{3}\right)=\frac{28}{21} \\ =\frac{2·2·7}{3·7} \left[\mathrm{divide} N\&D \mathrm{by} \mathrm{common} \mathrm{factor}7\right] \\ =\frac{2·2·\frac{7}{7}}{3·\frac{7}{7}} \\ =\frac{2·2}{3} \\ =\frac{4}{3} \end{gathered}$$