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Warm up
Determine if the set finite or infinite
1 Even numbers greater than 4 but less than 100
2 odd numbers3Fractions less than 14 -3 is a member of what group(s)5 Is a member of what group(s)2
Warm up Answers
1 Finite
2 Infinite
3 Infinite
4 integers rational real
5 irrational real
Lesson 12Properties of Real Numbers
Obj SWBAT
Justify manipulations of expressions using the properties of real numbers
Associative Property
The grouping of the numbers does not change the sum or the product
Additiona + (b + c) = (a + b) + c
Multiplication(amiddotb)middotc = amiddot(bmiddotc)
Hint The different GROUPS of numbers can all associate with each otherhellipthey are all
friends
Commutative Property
The order of the numbers does not change the sum or the product
Addition
a + b = b + a
Multiplication
amiddotb = bmiddotaNo matter how you flip
themhellipthe answer is always the same
Distributive Property
The term outside the parentheses can be multiplied by all the terms on the
inside of the parentheses
a(b + c) = (amiddotb) + (amiddotc)
a(b ndash c) = (amiddotb) ndash (amiddotc)
You distribute so that everyone gets an equal turnhellipget it
Identity Property of Addition
The sum of a number and zero is the number
a + 0 = a
Addition
+
Identity Property of Multiplication
The product of a number and one is the number
a 1 = a
Inverse Property of Addition
The sum of a number and its opposite is zero
-a + a =0
Inverse Property of Multiplication
The product of a number and its reciprocal is one
11
a
a 0a
When might you use this property in solving equations
Zero Product Property
The product of a number and zero is zero
a 0 = 0
Closure Property
The sum or product of any two real numbers is a unique real number
(If you add or multiply any two real numbers the sum or product is one
and only one real number)
a + b = real numbera b = real number
Summary
Write down two properties and tell how you will remember them
Classwork BD Book 1 pg 17 in class
Homework WS 13
Warm up Answers
1 Finite
2 Infinite
3 Infinite
4 integers rational real
5 irrational real
Lesson 12Properties of Real Numbers
Obj SWBAT
Justify manipulations of expressions using the properties of real numbers
Associative Property
The grouping of the numbers does not change the sum or the product
Additiona + (b + c) = (a + b) + c
Multiplication(amiddotb)middotc = amiddot(bmiddotc)
Hint The different GROUPS of numbers can all associate with each otherhellipthey are all
friends
Commutative Property
The order of the numbers does not change the sum or the product
Addition
a + b = b + a
Multiplication
amiddotb = bmiddotaNo matter how you flip
themhellipthe answer is always the same
Distributive Property
The term outside the parentheses can be multiplied by all the terms on the
inside of the parentheses
a(b + c) = (amiddotb) + (amiddotc)
a(b ndash c) = (amiddotb) ndash (amiddotc)
You distribute so that everyone gets an equal turnhellipget it
Identity Property of Addition
The sum of a number and zero is the number
a + 0 = a
Addition
+
Identity Property of Multiplication
The product of a number and one is the number
a 1 = a
Inverse Property of Addition
The sum of a number and its opposite is zero
-a + a =0
Inverse Property of Multiplication
The product of a number and its reciprocal is one
11
a
a 0a
When might you use this property in solving equations
Zero Product Property
The product of a number and zero is zero
a 0 = 0
Closure Property
The sum or product of any two real numbers is a unique real number
(If you add or multiply any two real numbers the sum or product is one
and only one real number)
a + b = real numbera b = real number
Summary
Write down two properties and tell how you will remember them
Classwork BD Book 1 pg 17 in class
Homework WS 13
Lesson 12Properties of Real Numbers
Obj SWBAT
Justify manipulations of expressions using the properties of real numbers
Associative Property
The grouping of the numbers does not change the sum or the product
Additiona + (b + c) = (a + b) + c
Multiplication(amiddotb)middotc = amiddot(bmiddotc)
Hint The different GROUPS of numbers can all associate with each otherhellipthey are all
friends
Commutative Property
The order of the numbers does not change the sum or the product
Addition
a + b = b + a
Multiplication
amiddotb = bmiddotaNo matter how you flip
themhellipthe answer is always the same
Distributive Property
The term outside the parentheses can be multiplied by all the terms on the
inside of the parentheses
a(b + c) = (amiddotb) + (amiddotc)
a(b ndash c) = (amiddotb) ndash (amiddotc)
You distribute so that everyone gets an equal turnhellipget it
Identity Property of Addition
The sum of a number and zero is the number
a + 0 = a
Addition
+
Identity Property of Multiplication
The product of a number and one is the number
a 1 = a
Inverse Property of Addition
The sum of a number and its opposite is zero
-a + a =0
Inverse Property of Multiplication
The product of a number and its reciprocal is one
11
a
a 0a
When might you use this property in solving equations
Zero Product Property
The product of a number and zero is zero
a 0 = 0
Closure Property
The sum or product of any two real numbers is a unique real number
(If you add or multiply any two real numbers the sum or product is one
and only one real number)
a + b = real numbera b = real number
Summary
Write down two properties and tell how you will remember them
Classwork BD Book 1 pg 17 in class
Homework WS 13
Associative Property
The grouping of the numbers does not change the sum or the product
Additiona + (b + c) = (a + b) + c
Multiplication(amiddotb)middotc = amiddot(bmiddotc)
Hint The different GROUPS of numbers can all associate with each otherhellipthey are all
friends
Commutative Property
The order of the numbers does not change the sum or the product
Addition
a + b = b + a
Multiplication
amiddotb = bmiddotaNo matter how you flip
themhellipthe answer is always the same
Distributive Property
The term outside the parentheses can be multiplied by all the terms on the
inside of the parentheses
a(b + c) = (amiddotb) + (amiddotc)
a(b ndash c) = (amiddotb) ndash (amiddotc)
You distribute so that everyone gets an equal turnhellipget it
Identity Property of Addition
The sum of a number and zero is the number
a + 0 = a
Addition
+
Identity Property of Multiplication
The product of a number and one is the number
a 1 = a
Inverse Property of Addition
The sum of a number and its opposite is zero
-a + a =0
Inverse Property of Multiplication
The product of a number and its reciprocal is one
11
a
a 0a
When might you use this property in solving equations
Zero Product Property
The product of a number and zero is zero
a 0 = 0
Closure Property
The sum or product of any two real numbers is a unique real number
(If you add or multiply any two real numbers the sum or product is one
and only one real number)
a + b = real numbera b = real number
Summary
Write down two properties and tell how you will remember them
Classwork BD Book 1 pg 17 in class
Homework WS 13
Commutative Property
The order of the numbers does not change the sum or the product
Addition
a + b = b + a
Multiplication
amiddotb = bmiddotaNo matter how you flip
themhellipthe answer is always the same
Distributive Property
The term outside the parentheses can be multiplied by all the terms on the
inside of the parentheses
a(b + c) = (amiddotb) + (amiddotc)
a(b ndash c) = (amiddotb) ndash (amiddotc)
You distribute so that everyone gets an equal turnhellipget it
Identity Property of Addition
The sum of a number and zero is the number
a + 0 = a
Addition
+
Identity Property of Multiplication
The product of a number and one is the number
a 1 = a
Inverse Property of Addition
The sum of a number and its opposite is zero
-a + a =0
Inverse Property of Multiplication
The product of a number and its reciprocal is one
11
a
a 0a
When might you use this property in solving equations
Zero Product Property
The product of a number and zero is zero
a 0 = 0
Closure Property
The sum or product of any two real numbers is a unique real number
(If you add or multiply any two real numbers the sum or product is one
and only one real number)
a + b = real numbera b = real number
Summary
Write down two properties and tell how you will remember them
Classwork BD Book 1 pg 17 in class
Homework WS 13
Distributive Property
The term outside the parentheses can be multiplied by all the terms on the
inside of the parentheses
a(b + c) = (amiddotb) + (amiddotc)
a(b ndash c) = (amiddotb) ndash (amiddotc)
You distribute so that everyone gets an equal turnhellipget it
Identity Property of Addition
The sum of a number and zero is the number
a + 0 = a
Addition
+
Identity Property of Multiplication
The product of a number and one is the number
a 1 = a
Inverse Property of Addition
The sum of a number and its opposite is zero
-a + a =0
Inverse Property of Multiplication
The product of a number and its reciprocal is one
11
a
a 0a
When might you use this property in solving equations
Zero Product Property
The product of a number and zero is zero
a 0 = 0
Closure Property
The sum or product of any two real numbers is a unique real number
(If you add or multiply any two real numbers the sum or product is one
and only one real number)
a + b = real numbera b = real number
Summary
Write down two properties and tell how you will remember them
Classwork BD Book 1 pg 17 in class
Homework WS 13
Identity Property of Addition
The sum of a number and zero is the number
a + 0 = a
Addition
+
Identity Property of Multiplication
The product of a number and one is the number
a 1 = a
Inverse Property of Addition
The sum of a number and its opposite is zero
-a + a =0
Inverse Property of Multiplication
The product of a number and its reciprocal is one
11
a
a 0a
When might you use this property in solving equations
Zero Product Property
The product of a number and zero is zero
a 0 = 0
Closure Property
The sum or product of any two real numbers is a unique real number
(If you add or multiply any two real numbers the sum or product is one
and only one real number)
a + b = real numbera b = real number
Summary
Write down two properties and tell how you will remember them
Classwork BD Book 1 pg 17 in class
Homework WS 13
Identity Property of Multiplication
The product of a number and one is the number
a 1 = a
Inverse Property of Addition
The sum of a number and its opposite is zero
-a + a =0
Inverse Property of Multiplication
The product of a number and its reciprocal is one
11
a
a 0a
When might you use this property in solving equations
Zero Product Property
The product of a number and zero is zero
a 0 = 0
Closure Property
The sum or product of any two real numbers is a unique real number
(If you add or multiply any two real numbers the sum or product is one
and only one real number)
a + b = real numbera b = real number
Summary
Write down two properties and tell how you will remember them
Classwork BD Book 1 pg 17 in class
Homework WS 13
Inverse Property of Addition
The sum of a number and its opposite is zero
-a + a =0
Inverse Property of Multiplication
The product of a number and its reciprocal is one
11
a
a 0a
When might you use this property in solving equations
Zero Product Property
The product of a number and zero is zero
a 0 = 0
Closure Property
The sum or product of any two real numbers is a unique real number
(If you add or multiply any two real numbers the sum or product is one
and only one real number)
a + b = real numbera b = real number
Summary
Write down two properties and tell how you will remember them
Classwork BD Book 1 pg 17 in class
Homework WS 13
Inverse Property of Multiplication
The product of a number and its reciprocal is one
11
a
a 0a
When might you use this property in solving equations
Zero Product Property
The product of a number and zero is zero
a 0 = 0
Closure Property
The sum or product of any two real numbers is a unique real number
(If you add or multiply any two real numbers the sum or product is one
and only one real number)
a + b = real numbera b = real number
Summary
Write down two properties and tell how you will remember them
Classwork BD Book 1 pg 17 in class
Homework WS 13
Zero Product Property
The product of a number and zero is zero
a 0 = 0
Closure Property
The sum or product of any two real numbers is a unique real number
(If you add or multiply any two real numbers the sum or product is one
and only one real number)
a + b = real numbera b = real number
Summary
Write down two properties and tell how you will remember them
Classwork BD Book 1 pg 17 in class
Homework WS 13
Closure Property
The sum or product of any two real numbers is a unique real number
(If you add or multiply any two real numbers the sum or product is one
and only one real number)
a + b = real numbera b = real number
Summary
Write down two properties and tell how you will remember them
Classwork BD Book 1 pg 17 in class
Homework WS 13
Summary
Write down two properties and tell how you will remember them
Classwork BD Book 1 pg 17 in class
Homework WS 13
