Pre Algebra Lesson 2 7

8/13/2019 Pre Algebra Lesson 2 7

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Multiplying Integers

Objective: Multiplying integers


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5-Minute Check

1. Use the pattern below to find the product of 48 X 52.

8 X 12 = 96

18 X 22 = 39628 X 32 = 896

38 X 42 = 1596


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5-Minute Check

1. Use the pattern below to find the product of 48 X 52.

8 X 12 = 96

18 X 22 = 39628 X 32 = 896

38 X 42 = 1596

48 X 52 = 2496


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5-Minute Check

Find the next two integers in each pattern

2. 5, 10, 20, 40, . . .


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5-Minute Check


2. 5, 10, 20, 40, . . . 80, 160


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5-Minute Check


2. 5, 10, 20, 40, . . .

3. -2, 6, -18, 54, . . .


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5-Minute Check


2. 5, 10, 20, 40, . . .

3. -2, 6, -18, 54, . . . -162, 486


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5-Minute Check

Give the next two letters in each pattern

4. N, O, R, S, V, . . .


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5-Minute Check


4. N, O, R, S, V, . . . W, Z


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5-Minute Check


4. N, O, R, S, V, . . .

5. J, F, M, A M J, J, A, . . .


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5-Minute Check


4. N, O, R, S, V, . . .

5. J, F, M, A M J, J, A, . . . S, O


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5-Minute Check


4. N, O, R, S, V, . . .

5. J, F, M, A M J, J, A, . . . S, O(September, October)


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5-Minute CheckFind a pattern that will allow you to finish

the following collection of numbers.

1 8 5 2 13 12 3 8 9

16 11 8 5 10 11 6 7 8

21 4 1 6 9 8 9 14 7

2 17 12 7 4 3 6 1 18

5 6 9 18 15 2 11 20 17

4 13 24 5 10 3 10

11 2 7 16 9

14 17 4

1


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2-7 Multiplying Integers

Example 1

Find the product of 6 and10.

You can solve this problem by looking for a pattern.6(20) = 120

6(10) = 60

6(0) = 0

6(-10) =

-60

-60

-60


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Example 1

Find the product of 6 and10.

You can solve this problem by looking for a pattern.6(20) = 120

6(10) = 60

6(0) = 0

6(-10) = -60

So, 6 X -10 = -60

-60

-60

-60


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The product of two integers with different signs is negative.


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Example 2

Solve p = -7(11)

p = -7(11) The two factors have different signs.


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Example 2

Solve p = -7(11)

p = -7(11) The two factors have different signs.

p = -77 The product is negative.


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The product of two integers with the same sign is positive.


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Example 3

Solve r = -8(-9)

r = -8(-9) The two factors have the same sign.


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Example 3

Solve r = -8(-9)

r = -8(-9) The two factors have the same sign.

r = 72 The product is positive.


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When we have a negative number such as-4, one can think of this as the opposite

of +4. So when we have a multiplication

problem such as -4 X 5, we can think of it

as the opposite of 4 X 5. 4 X 5 is 20.What is the opposite of 20? Our answer

would be negative 20. This is carried over

to this type of problem. -4 X (-5) We can

think of this as the opposite of 4 X (the

opposite of 5). We have already learned

that 4 X 5 is 20. 4 X the opposite of 5

would be negative 20 and then the

opposite of -20 is positive 20.

-(4 X 5)

-(4 X -(5))

-(-(20))

20


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When working with multiple factors, one can count thenumber of negative factors. If the number of negative factors

is odd, the product will be negative. If the number of negative

factors is even, the product will be positive.


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Example 4

Solve q = -2(-3)(-11)

q = -2(-3)(-11) There are three negative factors.

q = -2(-3)(-11) Three is odd.


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Example 4

Solve q = -2(-3)(-11)


q = -2(-3)(-11) Three is odd.

q = -2(33)

q = -66


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Example 4

Solve q = -2(-3)(-11)


q = -2(-3)(-11) Three is odd.

q = -2(33)

q = -66 The product will be negative.

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Pre Algebra Lesson 2 7