Warm Up Write each number as a percent.

-15, -7, -4, 0, 4, 7{…, -2, -1, 0, 1, 2, 3, …} Add the negative natural numbers to the whole numbers Integers Z 0, 4, 7, 15{0, 1, 2, 3, … } Add 0 to the natural numbers Whole Numbers W 4, 7, 15{1, 2, 3, …} These are the counting numbers Natural Numbers N ExamplesDescriptionName Key Concepts Subsets of the Real Numbers

This is the set of numbers whose decimal representations are neither terminating nor repeating. Irrational numbers cannot be expressed as a quotient of integers. Irrational Numbers I These numbers can be expressed as an integer divided by a nonzero integer: Rational numbers can be expressed as terminating or repeating decimals. Rational Numbers Q ExamplesDescriptionName Key Concepts Subsets of the Real Numbers

Rational Numbers The Real Numbers Irrational Numbers Integers Whole Numbers Natural Numbers The set of real numbers is formed by combining the rational numbers and the irrational numbers.

Example 1 Your math class is selling pies to raise money to go to a math competition. Which subset of real numbers best describes the number of pies p that your class sells?

Example 2 Classify and graph each number on a number line.

Example 3 Compare the two numbers. Use. a)-5, -8 b)1/3, c)3, √3

Key Concepts Let a, b, and c be real numbers. Opposite - (additive inverse) the opposite of any number a is -a. Reciprocal - (multiplicative inverse) the reciprocal of any nonzero number a is 1/a. PropertyAdditionMultiplication Commutative Associative Identity Inverse Distributive

Example 4 Name the property of real numbers illustrated by each equation. a)n · 1 = n b)a (b + c) = ab + ac c)4 + 8 = d)0 = q + (-q)

Example 5 Show each statement is false by providing a counterexample. a)The difference of two natural numbers is a natural number. b) The quotient of two irrational number is irrational. c) All square roots are irrational.

MACC.912.N-RN.2.3: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational, and the product of a nonzero rational number and an irrational number is irrational. ScoreLearning Progression 4I am able to use properties of real numbers to perform algebraic operations 3I am able to graph and order real numbers to identify properties of real numbers 2I am able to understand that real numbers have several special subsets related in particular ways 1I need prompting and/or support to complete tasks. Section Rate Your Understanding