1. Use the commutative properties.
a+b = b+a
a*b=b*a
2. Use the associative properties.
a+(b+c)= (a+b) +c
3. Use the identity properties. ID
a+0=a
a*1=a
4. Use the inverse properties.
5 → - 5
5 → 1/5
5. Use the distributive property.
100 (a+b+c) = 100a + 100b + 100c
Objectives: SWBT SWS
1.7 Properties of Real Numbers
Copyright © 2014, 2010, 2006 Pearson Education, Inc.
Section 1.7, Slide 1
Vocabulary - Concept - Formula
# | Term | Meaning |
1 | commutative | a+b = b+a Addition a*b=b*a Multiplication |
2 | associative | a+(b+c)= (a+b) +c |
3 | identity | a+0=a Addition a*1=a Multiplication |
4 | inverse | 5 → - 5 Addition 5 → ⅕ Multiplication |
5 | distributive | X (a+b+c) = Xa + Xb + Xc |
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Copyright © 2014, 2010, 2006 Pearson Education, Inc.
Section 4.1 Slide 3
Study Mathematics Skills
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2 Attend Class (70% of Success)
Be on Time
Pay attention
Take notes in your notebook
Ask questions and participate.
3 Home Work
Complete All assigned homework.
Do the quiz until you score 100%
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4-5 Before/During Test
practice test until Score 100%.
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Mini Lesson - Warm Up
Properties of Real Numbers
The commutative properties say that if two numbers
are added or multiplied in any order, they give the same
result.
Addition
Multiplication
Use the Commutative Properties
Example 1
Use a commutative property to complete each statement.
(a) –5 + 7 =
7 + ___
(–5)
(b) –3(8) =
8(___)
–3
Copyright © 2014, 2010, 2006 Pearson Education, Inc.
Section 1.7, Slide 7
The associative properties say that when we add or
multiply three numbers, we can group them in any
manner and get the same answer.
Addition
Multiplication
Use the Associative Properties
Example 2
Use an associative property to complete each statement.
(a) –6 + (–3 + 5) =
(–6 + ___) + 5
(–3)
(b) –3(5 · –2) =
(–3 ·___) · –2
5
Copyright © 2014, 2010, 2006 Pearson Education, Inc.
Section 1.7, Slide 8
Use
Commutative & Associative
Properties
Example 3 Find each sum or product.
(a) 18 + 23 + 9 + 12 + 27 + 11
= (18 + 12) + (23 + 27) + (9 + 11)
= 30 + 50 + 20
= 100
(b) 75 (9 · 4)
= (75 · 4) 9
= 300 · 9
= 2700
Easier
Copyright © 2014, 2010, 2006 Pearson Education, Inc.
Section 1.7, Slide 9
The identity properties say that the sum of 0 and any
number equals that number, and the product of 1 and
any number equals that number.
Addition
Multiplication
Use the Identity Properties
Example 4 Use an identity property to complete each statement.
Copyright © 2014, 2010, 2006 Pearson Education, Inc.
Section 1.7, Slide 10
Use the Identity Properties
Example 5 Write in lowest terms.
The product of a number and 1
is that number.
81/45
Copyright © 2014, 2010, 2006 Pearson Education, Inc.
Section 1.7, Slide 11
The opposite of a, –a, is the additive inverse of a.
The inverse property of addition says that the sum of a
number and its additive inverse is 0 (the additive identity).
Addition
Using the Inverse Properties
Copyright © 2014, 2010, 2006 Pearson Education, Inc.
Section 1.7, Slide 12
The reciprocal of a, 1/a, is the multiplicative inverse of the
nonzero number a.
The inverse property of multiplication says that the
product of a number and its multiplicative inverse is 1 (the
multiplicative identity).
Multiplication
Use the Inverse Properties
Example 6
Use an inverse property to complete each statement.
Addition
Multiplication
Copyright © 2014, 2010, 2006 Pearson Education, Inc.
Section 1.7, Slide 13
The distributive property says that multiplying a
number a by a sum of numbers b + c gives the same
result as multiplying a by b and a by c and then adding
the two products.
a(b + c) = ab + ac
The distributive property is also valid for subtraction.
a(b – c) = ab – ac
Use the Distributive Property
Example 7 Use the distributive property to rewrite each expression.
(a) –6(–2 + 5) =
–6(–2) + –6(5)
= 12 + (–30)
= –18
x
x
Copyright © 2014, 2010, 2006 Pearson Education, Inc.
Section 1.7, Slide 14
Example 7 Use the distributive property to rewrite each expression.
Use the Distributive Property
(b) 2(3x – 7)
2(3x) + 2(–7)
= 6x + (–14)
= 6x –14
(c) 3 · 9 + 3 · 6
Here, we can use the distributive property in reverse.
= 3(15)
= 45
(d) 5(2r – 3s + 4t)
5(2r) + 5(–3s) + 5(4t)
= 10r – 15s + 20t
= 3(9 + 6)
Reverse
Common
Copyright © 2014, 2010, 2006 Pearson Education, Inc.
Section 1.7, Slide 15
Practice
Makes
Perfect
Copyright © 2014, 2010, 2006 Pearson Education, Inc.
Section 1.2, Slide 16