1-1 Properties of Real Numbers1-1 Properties of Real Numbers

Objectives:Objectives:

• Identify the subsets of real numbers.Identify the subsets of real numbers.

• Identify the properties of real numbers.Identify the properties of real numbers.

• Find the opposite and reciprocal of a Find the opposite and reciprocal of a number.number.

• Place real numbers on a number line.Place real numbers on a number line.

VocabularyVocabulary

Natural Numbers – 1,2,3,4… the counting numbersNatural Numbers – 1,2,3,4… the counting numbers Whole Numbers – 0,1,2,3… the counting numbers & 0Whole Numbers – 0,1,2,3… the counting numbers & 0 Integers – …-2,-1,0,1,2… the whole numbers & negativesIntegers – …-2,-1,0,1,2… the whole numbers & negatives Rational Numbers – Integers & fractions & terminating or Rational Numbers – Integers & fractions & terminating or

repeating decimalsrepeating decimals Irrational Numbers – Non-terminal, non-repeating decimalsIrrational Numbers – Non-terminal, non-repeating decimals Real Numbers – all of the aboveReal Numbers – all of the above

More VocabularyMore Vocabulary

Additive Inverse – oppositeAdditive Inverse – opposite Multiplicative Inverse – reciprocalMultiplicative Inverse – reciprocal Absolute Value – how far a number is from 0Absolute Value – how far a number is from 0

PropertiesProperties

ExampleExample

Recreation – Many mathematical relationships involving Recreation – Many mathematical relationships involving variables are related to amusement parks. Which set of variables are related to amusement parks. Which set of numbers best describes the values for each variable?numbers best describes the values for each variable?

a.a. The cost The cost CC in dollars of admission for in dollars of admission for nn people. people.

The cost The cost CC of admission is a rational number (such as of admission is a rational number (such as $7.25), and the number $7.25), and the number nn of people is a whole number. of people is a whole number.

c.c. The park’s profit (or loss) The park’s profit (or loss) PP in dollars for each week in dollars for each week ww of of the yearthe year

The week number The week number ww is one of the first 52 natural is one of the first 52 natural numbers, and the profit (or loss) numbers, and the profit (or loss) PP is a rational number. is a rational number.

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Sample ProblemsSample Problems