Question

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

$\mathbf{36}\mathbf{\cdot }\mathbf{3}\frac{\mathbf{1}}{\mathbf{4}}$

Short answer

The value of the expression $36\cdot 3\frac{1}{4}$is 117.

Step-by-step solution

Step 1. Break 314 into simplest form.

Think of an equation whose sum or difference is $3\frac{1}{4}$.

$3\frac{1}{4}=3+\frac{1}{4}$

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:

$\begin{array}{l}36\cdot 3\frac{1}{4}=36\left(3+\frac{1}{4}\right)\\ =36\times 3+36\times \frac{1}{4}\end{array}$

Step 3. Evaluate the expression.

$\begin{array}{l}36\cdot 3\frac{1}{4}=36\times 3+36\times \frac{1}{4}\left[\text{Multiply}\right]\\ =108+9\left[\text{Add}\right]\\ =117\end{array}$