confidential 1 hello, natasha! this is mrs. bisanz. i will be your teacher today! our lesson:...

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Hello, Natasha!

This is Mrs. Bisanz. I will be your teacher today!

OUR LESSON: Multiplying Integers

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WARM-UP:

1.) 5 - 9 =

2.) 16 - (-20) =

3.) (-22) - 40 =

4.) (-65) - (-81) =

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Let's review what we learned in the last lesson.

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We are very familiar with Addition and it is easy for us to add

4 + 4 + 4 = 12

We can also think of this as three groups of 4 OR

3 x 4 = 12

Let's Get Started!

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0 4 8 12

On a number line, this might look like......

1 2 3

3 x 4 = 12

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So, let's look at

(-4) + (-4) + (-4) = -12

We know from our Addition Rules that when we add NEGATIVE numbers together, our sum is NEGATIVE.

We can also look at this as three groups of (-4) OR

3 x (-4) = -12

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On a number line, this might look like......

3 x (-4) = (-12)

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40-4-8-12

123

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But what happens when we multiply a NEGATIVE number by a NEGATIVE number??????

Multiplying by a NEGATIVE number is the opposite of multiplying by a POSITIVE number so our products have opposite signs.

If 3 x (-4) = -12

Then (-3) x (-4) = +12

Remember that a "product" is the answer to a multiplication problem.

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Rules for Multiplying Integers

The product of two integers with the SAME sign is always POSITIVE.

The product of two integers with DIFFERENT signs is always NEGATIVE.

6 x 7 = +42

(-5) x (-4) = +20

8 x (-4) = -32

(-9) x 3 = -27

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Let's try a few!

Remember:SAME SIGNS PositiveDIFFERENT SIGNS Negative

1.) -6 x 4 = (-24)

2.) 10 x -5 = (-50)

3.) (-8) x (-9) = 72

4.) 7 x 6 = 42

5.) -11 x 8 = -88

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When we multiply 3 or more numbers together, ......

(-4) x 5 x (-2) =

...we begin by multiplying 2 at a time and inserting the appropriate sign.

(-20) x (-2)

+40

(-4) x 5 x (-2) = +40

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You try some.

6 x (-10) x (-2) = 120

(-5) x 7 x 2

= -70

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Good! Now let's work with multi-digit numbers.

-47 x 583 =

5 8 3larger number of digits goes on top

4 7x

1

2

8

5

4 0

1

23

3

2 3 x

10

1

472 ,-

Let's review.

Multiply first and then add the appropriate sign. Also, remember your comma!

multiply from right to left

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You try this one!

(-62) x (-941) =

larger number of digits goes on topBe sure to add your COMMA and the appropriate sign.

2

9 4 1 X 6 2------------ 1 1

1 8 8 25 6 4 6 X------------5 8,3 4 2

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BREAK

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Game

Click here to play a game

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1.) Nancy lives 32 miles from her work. Howmany miles does she drive to and from workin a month? (Assume that a month has 4 weeksand Nancy works Monday through Friday.)

Total miles in a day 2 X 32 = 64 (to and fro)Total number of days in a month 5 X 4 = 20

so total miles in 20 days = 64 X 20 = 1280 miles

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2.) Erica baked chocolate chip cookies and broughtthem to her girl scout meeting. The girls ate halfthe cookies and the troop leaders ate 5 cookies. Erica took 15 cookies home with her after themeeting. How many cookies did she take to the

meeting?

Erica baked 40 cookies The girls ate 20 cookies (Half of what she got.) Troop leader ate 5 so she is left with 15.

40 -20 – 5 = 15

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3.) Susie has $232 in her bank account. Shemakes 3 withdrawals of $85 each. How muchmoney must she deposit back into the account

inorder to have a balance of $25?

Total money $232Withdrew $85 X 3 = 255.Balance = 232 – 255 = (-23)To get balance of $25 she needs to deposit25 – (-23) = $48

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Let's see how well you understood the lesson today!

1.) (-8) x 12 = -96

2.) (-6) x (-20) = 120

3.) 2 x (-5) x 4 = -40

4.) (-7) x (-3) x (-1) = -21

5.) 3 x (-3) x 2 x (-2) = 36

6.) 32 x (-4) = -128

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7.)

2,903 x (-31) =

2

2, 9 0 3 X 3 1 --------------- 2 9 0 3 8 7 0 9 X-------------- 8, 9 9 9 3

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Let's review what we learned today!

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Multiplying multi-digit numbers: 583 x (-47) =

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Great Job Today!

Remember to practice what you learned!

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