Warm Up: Multiplying and Dividing Remember to get out your Homework

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Warm Up Multiplying and DividingRemember to
get out your Homework!

• Multiply the following
• (-9)(8)
• (-4)(-12)
• (7)(-6)
• Divide the following

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Section 1.8 Notes

• The Distributive Property

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The Distributive Property

• For every real number a, b, and c,
• a(bc)abac (bc)abaca
• a(b-c)ab-ac (b-c)aba-ca
• Examples
• 5(206)5(20)5(6) (206)520(5)6(5)
• 9(30-2)9(30)-9(2) (30-2)930(9)-2(9)

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Using the Distributive Property for Mental Math

• You can separate large numbers into the sum or
  difference of numbers to assist in
  multiplication.
• Examples
• 34(102)34(1002) Rewrite 102 as 1002
• 34(100)34(2) Use the Distributive
  Property
• 340068 Simplify
  3468

You try. Simplify using mental math. 1. 13(103)
2. 21(101) 3. 24(98) 4. 15(99)
1339
2121
2352
1485
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Simplifying Expressions

• Use the Distributive Property to simplify an
  Algebraic Expression.
• Remember the simplest form has no grouping
  symbols (parenthesis, absolute value bars, etc).
• Simplify the expression 2(5x3)
• 2(5x3)2(5x)2(3) Use the Distributive Property
• 10x6 Simplify

You try. Simplify each expression. 1. 6(m5)
2. 2(3-7t) 3. (0.41.1c)(3)
6m30
6-14t
1.23.3c
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Using the Multiplication Property of 1

• To simplify an expression like (6x4), rewrite
  as
• 1(6x4) then use the multiplication property
  of 1.
• Simplify the expression (6x4)
• -(6x4)-1(6x4) Rewrite using -1
• -1(6x)(-1)(4) Use the Distributive
  Property
• -6x-4 Simplify

You try. Simplify each expression. 1. (2x1) 2.
(7-5b) 3. (3-8a)(-1)
-2x-1
-75b
3-8a
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Important Vocabulary

• Term-
• Constant-
• Coefficient-
• Like Terms-

a number, variable or the product of numbers and
variables
a term that has no variable.
a numerical factor of a term. (The number in
front of the variable)
have EXACTLY the same variable factors
Like Terms 3x and -2x -5x2 and 9x2 xy and
xy -7x2y3 and 15x2y3
Not Like Terms 8x and 7y 5y and 2y2 4y and
5xy x2y and xy2
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Combining Like Terms

• Simplify Each Expression
• 3x2 5x2
• 3x2 5x2(35) x2 Use the Distributive
  Property
• 8x2 Simplify

You try. Simplify each expression. 1. 7y6y 2.
3t-t 3. -9w-3w
13y
2t
-12w
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Writing an Expression

• You can write an expression from a verbal phrase.
• The word quantity indicates that two or more
  terms are within parentheses.
• Example
• Write an expression for 3 times the quantity x
  minus 5.
• Relate 3 times the quantity x minus 5
• Write 3 (x-5)
• Answer 3(x-5)

You Try. Write an expression for each phrase. a.
-2 times the quantity t plus 7 b. the product of
14 and the quantity 8 plus w
-2(t7)
14(8w)
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Practice Write at the Bottom of Your Notes!

• Use the Distributive Property to simplify 26(98)
• Simplify 3(4m-7)
• Simplify (5q-6)
• Simplify -2ww
• Write an expression for the product of 6 and
  the quantity 7 minus m.

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Jigsaw Activity Properties of Real Numbers

• On your desk is a card with numbers on it.
• The first number is your home group.
• The second number is your expert group.
• First, get with your expert group (the second
  number).
• Take 5 minutes to learn your expert property well
  enough to teach it to your home group.
• Make sure to write the property on a sheet of
  paper with examples to share with your group.
• Now, get with your home group.
• Each person has 3 minutes to describe the
  property to their group (I will tell you when it
  is time to switch).
• EVERYONE must write down notes about ALL
  properties. (You need to know them all fo.r your
  test!)

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Homework

• Assignment 8
• Textbook pg. 50-51 (2-48 Every OTHER Even) and
• Textbook pg. 56 (1-9)