Exercise 20 Page 20

Since mixed number notation indicates a fraction being added to a whole number, let's start by rewriting the problem. Notice that the fractions have the same denominator, so they can be added without any kind of manipulation. Let's rearrange the terms, add, and then simplify. $11+\frac{2}{3}$ is equal to the mixed number $11\frac{2}{3},$ which is our answer. Now let's name the property used in each step.

Step	Action	Property used
1	$a\frac{b}{c}=a+\frac{b}{c}$	Substitution
2	Commutative Property of Addition	Commutative (+)
3	Add parentheses	Associative (+)
4	Add terms	Substitution
5	Add fractions	Substitution
6	$\frac{a}{b}=\frac{a/3}{b/3}$	Substitution
7	$a+\frac{b}{c}=a\frac{b}{c}$	Substitution