Multiplying integers

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Multiplying integers

• By Rose Eisenmenger

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What Is Multiplication?

• A number of groups of a number
• Example 6 x 3 is the same as saying 6 groups of
  3
• This could be shown as

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What Is Multiplication?

• It could also be said in a word problem, Mary had
  5 friends coming over, and she wanted each
  person, including herself, to have 3 chocolates.
  How many chocolates would she need to buy?
• Therefore, multiplication can be shown as
• an equation
• 6 x 3
• word problem
• Mary had 5 friends
• picture

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Example 1 Multiplying A Positive By A Negative

• Lets try another problem using equation, word
  problem, and a picture
• Equation
• 6 x -4
• Word Problem
• Suzie owed 6 of her friends 4 dollars. How much
  money did she owe?

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Example 1Positive x Negative Picture

• Here are 6 boxes of 4, but we need six boxes of
  negative four
• Another way to say negative is, the opposite of,
  so we need the opposite of 4

Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
4
4
4
4
4
4
Since we are doing the opposite of 6 x 4 which
equals 24, our product will be the opposite! What
do you think the answer is?
-24
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Example 2Multiplying A Negative By A Positive

• We will also use an equation, word problem, and
  picture for this problem
• Equation
• -8 x 5
• Word Problem
• 8 people got a letter in the mail from the bank
  stating that they received 5. One week later,
  the same eight people got another letter saying
  that the bank made a mistake and meant to say
  that they owed the bank 5.

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Example 2Negative x Positive Picture

• Here are 8 boxes of 5, but we need negative 8
  boxes of 5
• Another way to say negative is, the opposite of,
  so we need the opposite of 8 boxes
• Since we are doing the opposite of 8 x 5 where we
  would get a positive answer, we will get an
  negative product. What do you think the answer is?

Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
5
5
5
5
5
5
5
5
-40
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Example 3Multiplying A Negative By A Negative

• Guess what? We are going to use the same method
  for this problem too!
• Equation
• -9 x -2
• Word Problem
• There were many people at the dog park, but only
  nine of the people brought two dogs each. All 18
  of those dogs found a way to escape under a
  fence, and became lost. The owners of the dogs
  went home dog-less and felt negative or sad.
  The next day, all the dogs returned home, which
  made the owners feel positive!

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Example 3 Negative x Negative

• We have 9 boxes of two, but we need negative nine
  boxes of negative two.
• Another way to say that is

Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
Opposite of
2
2
2
2
2
2
2
2
2
We have one opposite of for each negative
number per box Since there are two negative
numbers or Opposite of per box, they cancel
each other out Therefore, your answer will be
positive What do you think your answer will be?
18
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Lets Try Some!

• 6 x -7
• -8 x 4
• -3 x 5
• -6 x -1
• Challenge -2 x 0

-42
-32
-15
6
0
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Multiplying Integers Rules

• A positive times a negative equals a
  negative(pxn)
• A positive times a positive equals a positive
  (pxp)
• A negative times a negative equals a
  positive(nxn)
• Between the two factors and the product, there
  should either be 2 negative numbers or zero
  negative numbers