Q24. - Algebra 1

Question

Use the Distributive Property to rewrite each expression. Then evaluate.

$\mathbf{4}\frac{\mathbf{2}}{\mathbf{7}}\left(21\right)$

Step-by-Step Solution

Answer

The value of the expression $4\frac{2}{7}\left(21\right)$ is $\mathbf{90}$.

Step 1. Break 4 2 7 into simplest form.

Think of an equation whose sum or difference is $4\frac{2}{7}$.

$4\frac{2}{7}=4+\frac{2}{7}$

Step 2. Use the distributive property.

According to the distributive property, $\left(a\pm b\right)c=a\times c\pm b\times c$

So, the expression can be rewritten as follows:

$\begin{array}{l}4\frac{2}{7}\left(21\right)=\left(4+\frac{2}{7}\right)\left(21\right)\\ =4\times 21+\frac{2}{7}\times 21\end{array}$

Step 3. Evaluate the expression.

$\begin{array}{l}4\frac{2}{7}\left(21\right)=4\times 21+\frac{2}{7}\times 21 \left[\text{Simplify}\right]\\ =4\times 21+2\times 3 \left[\text{Multiply}\right]\\ =84+6 \left[\text{Add}\right]\\ =90\end{array}$