1.4 multiplication with negative numbers 1.5 division with negative numbers catherine conway math...
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1.4 MULTIPLICATION WITH NEGATIVE
NUMBERS1.5 DIVISION WITH
NEGATIVE NUMBERS
Catherine Conway Math 081
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MULTIPLICATION OF NEGATIVE NUMBERSEvaluate: -2 + -2 + -2 + -2 = ________
Repeated addition is the same thing as:_____________
...so -2 + -2 + -2 + -2 can be written:________
Evaluate: -4 + -4 + -4 = ______________
-4 + -4 + -4 can be rewritten:________
-8
Multiplication4(-2)
-12
3(-4)
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MULTIPLICATION OF NEGATIVE NUMBERSProblem: You are $30 in debt. If your
debt is increased 2 times, how much is your debt?
-30 x 2 = -60
Multiplying by a negative number is multiplying your debt.
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MULTIPLICATION OF NEGATIVE NUMBERSRULE #1:(positive number) × (negative number) =
___________________.
The _______________ property of multiplication allows me to multiply in any order.
So I also know that (negative number) × (positive number) = ___________________.
Negative Number
Commutative
Negative Number
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MULTIPLICATION OF NEGATIVE NUMBERSNegative × Positive = _________ and Positive × Negative = ___________
If the signs in a multiplication problem are different the solution is:_______________
I know that a: positive × positive = ______________
Now follow the pattern:
(+)(–) = ____________ (+)(+) = ______________
(–)(+) = ____________ (–)(–) = ______________
I know that a: negative × negative = ______________
If the signs in a multiplication problem are the same the solution is:_______________
NegativeNegative
Negative
Positive
Negative
Negative
Positive
Positive
Positive
Positive
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PRACTICE Pg117-120 #20, 22, 24 (exponents)
#34, 38, 42, 44, 46, 50, 54 (order of operation)
#61, 67 (application)
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PG117 #20, 22, 24
20) -2(-3)(-4)
22) a. (-5)2 b. -52
24) a. (-4)3 b. -43
-24
(-5)(-5) = 25 -(5)(5) = -25
(-4)(-4)(-4) = -64 -(4)(4)(4) = -64
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PG 118#34, 38, 42, 44, 46, 50, 54 34) 7(-6 + 3)
38) -7 + 3(6 – 2)
42) 6(-1) + 2(-7)
44) 2(-1)(-3) + 4(-6)
46) (9 – 3)(2 – 6)
50) -2(8 – 10) + 3(4 – 9)
54) 4(-3)(2 – 5)
-21
5
-20
-18
-24
-11
36
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PG 118 #61 61)
100(-2) + 50(8)-200 + 400
200
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PG 120 #67 67
0
-7
0
3
2-2
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DIVISION OF NEGATIVE NUMBERS
ac
b ______ ______ _______
______ 5 40
40______
5
The Division Algorithm: If then
Example 1: Negative divided by a Positive:
so…
Negative divided by a positive will always result in a:______________
c b a
-8
-8
Negative
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DIVISION OF INTEGERSWait a minute…these look familiar!
These are the same rules as:__________________
If the signs in a division problem are different the solution is:______________
If the signs in a division problem are the same the solution is:_____________
Negative
Multiplication
Positive
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SUMMARY OF NEGATIVE NUMBERS
Multiplication of negative numbers
Division of negative numbers
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PRACTICE Pg125-126 #4, 10, 14, 16 (division)
#22, 26, 30, 34, 40 (order of operation)
#61-63 (averages)
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PG125#4, 10, 14, 16 (DIVISION)
-5 0
-3 16
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PG125#22, 26, 30, 34, 40 (ORDER OF OPERATIONS)
1
2-7
252
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PG 126#61-63 (AVERAGES)
0
0
0 2 2