Chapter 1.1, Problem 59E

To determine

To simplify the below expression using the Distributive Property −

  $\frac{5}{6}\left(x+\frac{1}{2}+4\right)$

Answer to Problem 59E

The simplified expression is $\frac{5}{6}x+\frac{15}{4}$ .

Explanation of Solution

Given:

Expression: $\frac{5}{6}\left(x+\frac{1}{2}+4\right)$

Formula Used:

According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Calculation:

Given:

Expression: $\frac{5}{6}\left(x+\frac{1}{2}+4\right)$

Solving the above expression using the distributive property, we have:

  $\begin{array}{l}\frac{5}{6}\left(x+\frac{1}{2}+4\right)=\frac{5}{6}\left(x\right)+\frac{5}{6}\left(\frac{1}{2}\right)+\frac{5}{6}\left(4\right)\\ \frac{5}{6}\left(x+\frac{1}{2}+4\right)=\frac{5}{6}x+\frac{5}{12}+\frac{10}{3}\\ \frac{5}{6}\left(x+\frac{1}{2}+4\right)=\frac{5}{6}x+\frac{5+40}{12}\\ \frac{5}{6}\left(x+\frac{1}{2}+4\right)=\frac{5}{6}x+\frac{45}{12}\\ \frac{5}{6}\left(x+\frac{1}{2}+4\right)=\frac{5}{6}x+\frac{15}{4}\end{array}$

Hence, the simplified expression is $\frac{5}{6}x+\frac{15}{4}$ .

Conclusion:

Hence, the simplified expression is $\frac{5}{6}x+\frac{15}{4}$ .