Chapter 7, Problem 1CR

To determine

Expression $\frac{7}{8}\left(8+5\right)$ as equivalent numeric expression and then evaluate

Answer to Problem 1CR

  $\frac{91}{8}$

Explanation of Solution

Given information:

The expression, $\frac{7}{8}\left(8+5\right)$

Concept used:

• The distributive property of binomials (FOIL):

    $\left(a+b\right)\left(c+d\right)=a\cdot c+a\cdot d+b\cdot c+b\cdot d$

• Left Distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$
• Exponent property: $x^n\cdot x^m=x^{n+m}$

Calculation:

In order to simplify the given expression, use the left distributive property and simplify the like terms as shown below

  $\begin{array}{c}\frac{7}{8}\left(8+5\right)\\ =\frac{7}{8}\cdot 8+\frac{7}{8}\cdot 5\\ =\frac{56}{8}+\frac{35}{8}\\ =\frac{91}{8}\end{array}$

Thus, the given expression as an equivalent expression is to $\frac{91}{8}$