1. 1.4 MULTIPLICATION WITH NEGATIVE NUMBERS 1.5 DIVISION WITH NEGATIVE NUMBERS Catherine Conway Math 081

2. MULTIPLICATION OF NEGATIVE NUMBERS Evaluate: -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 Multiplication 4(-2) -12 3(-4)

3. MULTIPLICATION OF NEGATIVE NUMBERS Problem: You are $30 in debt. If your debt is increased 2 times, how much is your debt? -30 2 = -60 -30 x 2 = -60 Multiplying by a negative number is multiplying your debt. Multiplying by a negative number is multiplying your debt.

4. MULTIPLICATION OF NEGATIVE NUMBERS RULE #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

5. MULTIPLICATION OF NEGATIVE NUMBERS Negative × 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:_______________ Negative Positive Negative Positive

6. PRACTICE Pg117-120 #20, 22, 24 (exponents) #34, 38, 42, 44, 46, 50, 54 (order of operation) #61, 67 (application)

7. PG117 #20, 22, 24 20) -2(-3)(-4) 22) a. (-5) 2 b. -5 2 24) a. (-4) 3 b. -4 3 -24 (-5)(-5) = 25-(5)(5) = -25 (-4)(-4)(-4) = -64-(4)(4)(4) = -64

8. 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

9. PG 118 #61 61) 100(-2) + 50(8) -200 + 400 200

10. PG 120 #67 67 0 -7 0 3 2 -2

11. DIVISION OF NEGATIVE NUMBERS The Division Algorithm: If then Example 1: Negative divided by a Positive: so… Negative divided by a positive will always result in a:______________ cba -8 Negative

12. DIVISION OF INTEGERS Wait 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

13. SUMMARY OF NEGATIVE NUMBERS Multiplication of negative numbers Division of negative numbers

14. PRACTICE Pg125-126 #4, 10, 14, 16 (division) #22, 26, 30, 34, 40 (order of operation) #61-63 (averages)

15. PG125 #4, 10, 14, 16 (DIVISION) -5 0 -3 16

16. PG125 #22, 26, 30, 34, 40 (ORDER OF OPERATIONS) 1 2 -7 25 2

17. PG 126 #61-63 (AVERAGES) 0 0 022