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L 2.5 Warm-Up Exercises
FIND THE SUM OF THE MATRICES.
5 7-
2- 4
4 8
2- 3-
2.5 Multiplying Real Numbers
Multiplication RulesObjective: To multiply positives and negatives, including decimals and fractions!!
1. (6)(-4) 2. -4c (5d)
3. (-1)(-12) 4. 12 (-3)
5. - 2 -11 6. (7)(-7)
7. 8 (-3)(2) 8. -2 -6 -4
9. (-3b)(-4b)(-2z)(-5z)(-1)
Does the number of negative values(signs) affect the sign of the product? How?
Same signs “+”Diff. signs “–”Even “-” signs “+”Odd “-” signs “–”
-24 -20cd
-12 -36
22 -49
-48 -48
-120 b2z2
Multiplying Decimals What is the rule for multiplying
decimals?
Try these: Don’t forget the sign!!
10. (2.4)(-3.1) 11. 4.2(1.14) 12. (-5.3)(-0.04)
13. (2.93)(0.012) 14. (-10)(3.56)(-2)
Line up at the right and multiply as whole number, when finished, place decimal point from right for the total number of decimal digits.
-7.44 4.788 0.212
0.03516 71.2
5 Minute Brain Break
USE THIS TIME TO relax and/or STETCH OUT….
Try this Brain Puzzle…
In each sentence, an animal is concealed. The first sentence has dog concealed. Can you find the others?
1. What shall I do, Gertrude?2. Asking nutty questions can be most annoying.3. A gold key is not a common key.4. Horace tries in school to be a very good boy.5. People who drive too fast are likely to be arrested.6. Did I ever tell you, Bill, I once found a dollar?7. John came late to his arithmetic class.8. I enjoy listening to music at night.
Multiplying Fractions
Try these: Don’t forget the sign!!
15. 16. 17.
18. 19.
5
3
3
2
1833
116
43
76
127
21
2553 c3
c245
n6
What is the rule for multiplying fractions?
What should you do to make whole numbers look like
fractions?
Diagonally or vertically cancel the greatest common factor between any numerator and denominate and then multiply the numerators and denominates.
Just put a dummy denominate “1”.
2
51
15
4n3
3
8
Properties of Multiplication
Properties of Multiplication
Definition Example
Commutative a · b = b · a
Associative (a · b) · c = a ·(b · c)
Identity a · 1 = a
4 · (-2) = (-2) · 4
[(-4) · 3] · (-2) = (-4) · [ 3 · (-2)]
(-2) · 1 = -2
Ex. (2) (–x) = –2x 3 (–n)(–n) = 3n2
–(y)4 = –(y·y·y·y) = –y4
Multiplying
NegativeX
Negative
PositiveX
Positve
DecimalsFractions
POSITIVE!
Straight Across
I
Ignore DecimalsCount Numbers
Behind DecimalsTo Figure Out
Where DecimalGoes
Whole Numbers
PositiveX
Negative
NegativeX
Positive
NEGATIVE!
Summary
Daily Homework Quiz
Find the Product.
1.(-2)(8)(-1)2.(7)(-3)(-5)(-1/2)
3. Evaluate a³ + 2a² - a when a = -2
In-Class AssignmentTextbook Pages 96
#’s 16-49 (All)