1.9 Properties of Real Numbers

Learning Objectives

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

  • Use the commutative and associative properties
  • Use the identity and inverse properties of addition and multiplication
  • Use the properties of zero
  • Simplify expressions using the distributive property

When we have to simplify algebraic expressions, we can often make the work easier by applying the commutative or associative property first, instead of automatically following the order of operations. When adding or subtracting fractions, combine those with a common denominator first.

Using the distributive property as shown in Example 1.134 will be very useful when we solve money applications in later chapters.

All the properties of real numbers we have used in this chapter are summarized in Table 1.57.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.This is a table that has five rows and four columns. In the first row, which is a header row, the cells read from left to right “I can…,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can…” reads “use the commutative and associative properties,” “use the identity and inverse properties of addition and multiplication,” “use the properties of zero,” and “simplify expressions using the distributive property.” The rest of the cells are blank.

ⓑ After reviewing this checklist, what will you do to become confident for all objectives?