Q21. - Algebra 1

Question

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

$7\cdot 497$

Step-by-Step Solution

Answer

The value of the expression $7\cdot 497$ is $\mathbf{3479}$.

Step 1. Break 497 into the simplest form.

Think of an equation whose sum or difference is 497. 

$497=500-3$

Step 2. Use the distributive property.

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

So, the expression can be rewritten as follows:

$\begin{array}{l}7\cdot 497=7\left(500-3\right)\\ =7\times 500-7\times 3\end{array}$

Step 3. Evaluate the expression.

$\begin{array}{l}7\cdot 497=7\times 500-7\times 3 \left[Multiply\right]\\ =3500-21 \left[Subtract\right]\\ =3479\end{array}$