### Learning Outcomes

By the end of this section, you will be able to:

- Identify rational and irrational numbers from a list of numbers.
- Classify real numbers as counting, whole, rational, irrational, or integers.
- Identify the associative and commutative properties of addition and multiplication.
- Use the associative and commutative properties of addition and multiplication to rewrite algebraic expressions.
- Evaluate algebraic expressions for a given value using the commutative and associative properties of addition and multiplication.
- Simplify algebraic expressions using the commutative and associative properties of addition and multiplication.
- Apply the distributive property to simplify an algebraic expression involving whole numbers, integers, fractions and decimals.
- Simplify and evaluate an algebraic expression using the distributive property.
- Identify the multiplication and division properties of zero.
- Identify and use the identity properties of multiplication and addition.
- Simplify algebraic expressions using identity, inverse and zero properties.

Earlier, when studying fractals, you learned how to use the distributive property of real numbers to multiply polynomial expressions together. The distributive property is one of three important properties of real numbers: associative, commutative, and distributive. With these properties, we are able to creatively re-represent variable expressions in helpful ways in order to accomplish a quantitative task or calculation. As you prepare now to study set theory and logic, it will be important to develop a deeper understanding of the properties of real numbers. That’s the focus of this review section — the properties of real numbers.

### Recall for success

Look for red boxes like this one throughout the text. They’ll show up just in time to give helpfulĀ reminders of the math you’ll need, right where you’ll need it.