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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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.
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Warm UpWrite each number as a percent.
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-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
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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
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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.
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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?
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Example 2Classify and graph each number on a number
line.
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Example 3Compare the two numbers. Use < and >.
a) -5, -8
b) 1/3, 1.333
c) 3, √3
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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
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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)
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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.
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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