To graph and order real numbers To identify properties of real numbers. Algebra 2 Foundations, pg 11
To graph and order real numbers To identify properties of real numbers. In the Solve It, you classified sets of emoticons. In this lesson, you will classify real numbers into special subsets that are related in particular ways. Focus Question How are the real numbers classified? Algebra 2 Foundations, pg 11 The real numbers consist of __________________ and ___________________. The rational numbers include ______________________________________________. rational numbers irrational numbers Integers, whole numbers, and natural numbers
“You can graph every real number as a point on the number line. Algebra 2 Foundations, pg 11 To graph and order real numbers To identify properties of real numbers.
Algebra 2 Foundations, pg 12 To graph and order real numbers To identify properties of real numbers.
Algebra 2 Foundations, pg 12 To graph and order real numbers To identify properties of real numbers. “You can classify a variable by naming the subset of the real numbers that gives you the most information about the numbers the variable represents. Classifying a Variable Multiple Choice: Your school is sponsoring a charity race. Which set of numbers best describes the number of people p who participate in the race? Problem 1
1.In Problem 1, if each participant made a donation d of $15.50 to a local charity, which subset of real numbers best describes the amount of money raised in dollars? Would the answer change if you refer to the amount of money in pennies rather than in dollars? Got it? Algebra 2 Foundations, pgs 12 To graph and order real numbers To identify properties of real numbers. The donation d of $15.50 belongs to the set of Rational numbers. The number ends in a terminating decimal. Yes pennies is best described by the set of natural numbers.
Algebra 2 Foundations, pg 13 To graph and order real numbers To identify properties of real numbers. Graphing Numbers on the Number Line What is the graph of the numbers – 5/2, √2, 2.6 ? Problem 2 2.What is the graph of the numbers √3, 1.4, 1/3 ? Got it?
Comparing Real Numbers Problem 3 Algebra 2 Foundations, pg 13 To graph and order real numbers To identify properties of real numbers. “The number line is helpful for ordering several real numbers. It is easier to compare two numbers with one of the _____________ symbols, > or <. inequality
To graph and order real numbers To identify properties of real numbers. Focus Question Why are the properties of real numbers important? Algebra 2 Foundations, pg 11 The properties of real numbers are relationships that are true for all real numbers except _____. Zero is the additive identity for the real numbers. For example, = 2. Zero is the only real number that has no ______________ _________. No number times 0 equals 1. zero multiplicative inverse You use the properties of real numbers for all math problems that involve real numbers.
To graph and order real numbers To identify properties of real numbers. Algebra 2 Foundations, pg 14 “The _________ or _______________ of any number a is –a. The sum of a number and its opposite is ____, the ________________. Examples: 12 + (-12) = = 0 The ___________ or ____________________ of any nonzero number a is. The product of a number and its reciprocal is ___, the _____________________. Examples: opposite additive inverse 0 additive identity reciprocal multiplicative inverse 1 multiplicative identity 1a1a 1818 = 1 -5 =
To graph and order real numbers To identify properties of real numbers. Algebra 2 Foundations, pg 14
To graph and order real numbers To identify properties of real numbers.
To graph and order real numbers To identify properties of real numbers.