Warm Up Write each number as a percent. -15, -7, -4, 0, 4, 7{…, -2, -1, 0, 1, 2, 3, …} Add the...
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Transcript of Warm Up Write each number as a percent. -15, -7, -4, 0, 4, 7{…, -2, -1, 0, 1, 2, 3, …} Add the...
Section 1.2Properties of Real
Numbers
Common Core State Standards: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.
Warm UpWrite 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
IntegersZ
0, 4, 7, 15{0, 1, 2, 3, … } Add 0 to the natural numbers
Whole NumbersW
4, 7, 15{1, 2, 3, …}These are the counting numbers
Natural NumbersN
ExamplesDescriptionName
Key ConceptsSubsets 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 NumbersI
These numbers can be expressed as an integer divided by a nonzero integer:Rational numbers can be expressed as terminating or repeating decimals.
Rational NumbersQ
ExamplesDescriptionName
Key ConceptsSubsets 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 1Your 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 2Classify and graph each number on a number
line.
Example 3Compare the two numbers. Use < and >.
a) -5, -8
b) 1/3, 1.333
c) 3, √3
Key ConceptsLet 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.
Property Addition Multiplication
Commutative
Associative
Identity
Inverse
Distributive
Example 4Name the property of real numbers illustrated by each
equation.
a) n · 1 = n
b) a (b + c) = ab + ac
c) 4 + 8 = 8 + 4
d) 0 = q + (-q)
Example 5Show 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.
Score Learning Progression
4 I am able to • use properties of real numbers to perform algebraic
operations
3 I am able to• graph and order real numbers• to identify properties of real numbers
2 I am able to • understand that real numbers have several special
subsets related in particular ways
1 I need prompting and/or support to complete tasks.
Section 1.2 - Rate Your Understanding