1.4 MULTIPLICATION WITH NEGATIVE

NUMBERS1.5 DIVISION WITH

NEGATIVE NUMBERS

Catherine Conway Math 081

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)

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.

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

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

PRACTICE Pg117-120 #20, 22, 24 (exponents)

#34, 38, 42, 44, 46, 50, 54 (order of operation)

#61, 67 (application)

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

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

PG 118 #61 61)

100(-2) + 50(8)-200 + 400

200

PG 120 #67 67

0

-7

0

3

2-2

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

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

SUMMARY OF NEGATIVE NUMBERS

Multiplication of negative numbers

Division of negative numbers

PRACTICE Pg125-126 #4, 10, 14, 16 (division)

#22, 26, 30, 34, 40 (order of operation)

#61-63 (averages)

PG125#4, 10, 14, 16 (DIVISION)

-5 0

-3 16

PG125#22, 26, 30, 34, 40 (ORDER OF OPERATIONS)

1

2-7

252

PG 126#61-63 (AVERAGES)

0

0

0 2 2