1.1.2 Properties of Real Numbers
Key Objectives • Identify and use properties of real numbers. • Use mental math in real world applications. • Classify statements as sometimes, never, or always true. Key Terms • An additive inverse is the opposite of a number. Two numbers are additive inverses if their sum is zero. • The multiplicative inverse of a nonzero number is the number's reciprocal. • The Associative Property is the property that states that three or more values being added or multiplied together can be grouped in any order without changing the result. ( a + b ) + c = a + ( b + c ) ( a ⋅ b ) ⋅ c = a ⋅ ( b ⋅ c ) • The Distributive Property is the property that states that the product of a value and a sum (or difference) is equal to that value multiplied by each of the values being added (or subtracted). The four basic math operations are addition, subtraction, multiplication, and division. Recall that the opposite of any number a is − a and the reciprocal of any nonzero number a is 1/ a . Because subtraction is addition of the opposite and division is multiplication by the reciprocal, the properties of real numbers focus on addition and multiplication. Example 1 Finding Inverses The opposite of a number can also be called its additive inverse. The sum of a number and its additive inverse is always 0. The reciprocal of a nonzero number can also be called its multiplicative inverse. The product of a nonzero number and its multiplicative inverse is always 1. a ( b + c ) = ab + ac a ( b − c ) = ab − ac • A commission is a fee paid to a person who negotiates a sale. • A counterexample is an example that shows that a statement is false.
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