Transcript Multiplication of Real Numbers

2.5 Multiplication of Real Numbers
GOAL
1
MULTIPLYING REAL NUMBERS
Rules for multiplying two real numbers:
positive
•If the signs are the same, the product is _______.
negative
•If the signs are different, the product is ________.
EXAMPLE 1
Extra Example 1
Find the product.
a. (9)(–3)
-27
 1
b. (8)    ( 6)
 2
(–4)(–6)
24
c.
(–3)3
(–3)(–3)(–3)
(9)(–3)
–27
 1
d. ( 2)    ( 3)( 5)
 2
1(–3)(–5)
(–3)(–5)
15
EXAMPLE 2
Extra Example 2
Find the product.
a. (–n)(–n) Two negative signs: n2
b. (–4)(–x)(–x)(x) Three negative signs: –4x3
c. –(b)3
One negative sign: –(b)(b)(b) = –b3
d. (–y)4
Four negative signs: (–y)(–y)(–y)(–y) = y4
SUMMARY: An even number of negative signs results in a
positive product, and an odd number of
negative signs results in a negative product.
PROPERTIES OF MULTIPLICATION
•COMMUTATIVE PROPERTY
Order doesn’t matter.
•ASSOCIATIVE PROPERTY
Grouping doesn’t matter.
•IDENTITY PROPERTY
a times 1 equals a.
•PROPERTY OF ZERO
a times 0 equals 0.
•PROPERTY OF OPPOSITES
a times –1 equals –a.
EXAMPLE 3
Extra Example 3
Evaluate the expression when x = –7.
a. 2(–x)(–x)
2  ( 7)  ( 7) 
OR simplify first:
2  7  7 
14  7 
98
2(–x)(–x)
2x2
2(-7)2
2(49)
98
Extra Example 3 (cont.)
Evaluate the expression when x = –7.
b.
 2

5

x

  
 7
 2
 5( 7)   
 7
 2
35   
 7
10
OR use the associative property:
 2

5

x

  
 7
 2

5(

7)

  
 7
  2 
5  7    
  7 
5(2)
10
Checkpoint
Find the product.
1. (–2)(4.5)(–10)
90
2. (–4)(–x)2
–4x2
3. Evaluate the expression when x = –3:
(–1• x)(x)
–9
2.5 Multiplication of Real Numbers
GOAL
2
USING MULTIPLICATION IN REAL LIFE
VOCABULARY
•displacement— The change in the position of an object.
May be negative, positive, or zero, while
distance may only be positive or zero.
EXAMPLE 4
Extra Example 4
A leaf floats down from a tree at a velocity of –12 cm/sec.
Find the vertical distance traveled in 4.2 sec.
VERBAL
MODEL
Vertical
= Velocity • Time
displacement
LABELS
d
ALGEBRAIC
MODEL
SOLVE
–12 cm/sec 4.2 sec
cm 

d   12
(4.2 sec)

sec 

d = –50.4 cm
The leaf has a vertical displacement of –50.4 cm,
or 50.4 cm downward.
EXAMPLE 5
Extra Example 5
A grocery store runs a sale where customers can get two
bags of spinach for the price of one. The store normally
charges $1.69 per bag. How much will they be losing in
sales if they give away 798 free bags?
VERBAL
MODEL
LABELS
ALGEBRAIC
MODEL
SOLVE
Loss = Number
of bags
a
798
•
Loss
per bag
$1.69
 $1.69 
a   798 bags  

bag


a = $1348.62
The store loses $1348.62.
Checkpoint
1. A paper airplane descends at a velocity of –14 in./sec.
Find the vertical distance traveled in 7.5 sec.
–105 in.
2. After a recent flood, a store owner sells 294 cans of
green beans at a reduced price because their labels were
ruined. Because the price the store originally paid for the
beans is more than the reduced price, the store loses $0.12
on each can of beans sold. How much will the store lose if
it sells all 294 cans of beans?
$35.28
QUESTIONS?