Multiplication and Division of Integers

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Section 4.2

• Multiplication and Division of Integers

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Signs

• What is a negative times a positive?
• What is a negative times a negative?

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Multiplication of Signed Numbers

• ()() ()
• ()(-) (-)
• (-)() (-)
• (-)(-) ()

• When something good happens to somebody good
  thats good.
• When something good happens to somebody bad
  ...thats bad.
• When something bad happens to somebody good
  ...thats bad.
• When something bad happens to somebody bad
  ...thats good.

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Multiplication of Signed NumbersFill in the Blank

• The product of two negative numbers is a
  __________ number.

positive
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Multiplication of Signed NumbersFill in the Blank
positive
negative

• The product of a _________ number and a _________
  number is a negative number.

positive
negative
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Multiplication of Signed NumbersFill in the Blank

• When the sum of two negative numbers is
  multiplied by a positive number, the product is a
  _______ number.

negative
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Multiplication of Signed NumbersFill in the Blank

• When the sum of two positive numbers is
  multiplied by a negative number, the product is
  a _______ number.

negative
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Multiplication of Signed NumbersFill in the Blank

• When a negative number is squared, the result is
  a _________ number.

positive
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Multiplication of Signed NumbersFill in the Blank

• When a negative number is raised to the fifth
  power, the result is a _________ number.

negative
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Exponents

• (-1)3
• (-1)(-1)(-1)
• (1)(-1)
• -1

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What is the sign?

• (-1)2
• (-1)3
• (-1)4
• (-1)5
• (-1)6
• (-1)7
• (-1)8

• Positive
• Negative
• Positive
• Negative
• Positive
• Negative
• Positive

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Properties of Integer Multiplication

• Given integers a, b, and c
• Closure
• ab is a unique integer

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Properties of Integers

• Given integers a, b, and c
• Commutative
• ab ba

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Properties of Integers

• Given integers a, b, and c
• Associative
• (a b)c a(bc)

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Properties of Integers

• Given integers a, b, and c
• Identity element of addition
• 0 a a 0 a
• Identity element of multiplication
• 1 a a 1 a

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Distributive Properties of Multiplication over
Addition for Integers

• a(b c) ab ac

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Distributive Properties of Multiplication over
Subtraction for Integers

• a(b - c) ab - ac

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Uniqueness property of the Additive Inverse

• For every integer a there exists a unique integer
  a, such that
• a -a 0 -a a
• What is the parallel for multiplication?

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Now try this 4- 3

• Determine how to use the difference of squares
  formula to compute the following mentally
• 22 18
• 24 36
• 998 1002

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Definition of Integer Division

• If a and b are integers with
• b ? 0,
• then a b is the unique integer c,
• if it exists,
• such that a bc.

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Order of Operations
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Section 4.2 Homework

• Multiplication Division of Integers
• Pg 211 5,6,7,12,13,16,17,18,20
• Section 4.3 Divisibility pg 223-226
• 2ace,3,4,6,11,18,20,29,37,38