Download Multiplication and Division of Real Numbers

MTH 11203
Algebra
MULTIPLICATION AND DIVISION
OF REAL NUMBERS
CHAPTER 1 SECTION 8
Multiply Numbers
 The Sign of the Product of Two Real Numbers
 Rule 1: The product of two numbers with like signs is a
positive number
(-) · (-) = +
(+) · (+) = +

Rule 2: The product of two numbers with unlike signs is a
negative number
(+) · (-) = (-) · (+) = -
 Multiplication and division of decimals are covered in
appendix A.
Multiply Numbers
 Example # 18:
-4(2) = -8
neg. because different signs
 Example # 20:
6(-2) = -12
neg. because different signs
 Example # 21:
(-8)(-10) = 80
 Example:
(6)(-9) = -54 neg. because different signs
pos. because same signs
Multiply Numbers
 Example:
(-8)(-4) = 32
 Example:
(0)(-8) = 0
 Example:
(-4)(-6) = 24
pos. because same signs
0 is never pos. or neg.
pos. because same signs
 Careful not to confuse subtraction with multiplication
Example
-4 – 5
-4 + (-5)
-9
(-4)(-5)
20
Multiply Numbers
 Example
 1  5  (1)(5) 5

   
(6)(7)
42
 6  7 
 Example
1
 1  3  (1)(3) 3 1


or    
5
 3  5  (3)(5) 15 5
 Remember that negatives can be written different ways
a
b
a
a
or
or b
b
Multiply Numbers
 Multiplication of more that one number in a given problem:
 Helpful hint:
Even number of negatives will equal a positive result
 Odd number of negatives will equal a negative result

 Example # 90 pg 67:
4(-2)(-1)(-5)
(-8)(-1)(-5)
(8)(-5)
-40
Odd negatives equals negative results
Multiply Numbers
 Example :
(-3)(2)(-1)(-2)(-4)
(-6)(-1)(-2)(-4)
(6)(-2)(-4)
(-12)(-4)
48
 Example :
(-3)(4)(-9)(-3)
(-12)(-9)(-3)
(108)(-3)
-324
Even negatives equals
positive results
Odd negatives equals
Negative results
Multiply Numbers
 Example :
(-2)(4)(-1)(-3)(-5)
(-8)(-1)(-3)(-5)
(8)(-3)(-5)
(-24)(-5)
120
Even negatives equals
positive results
Divide Numbers
 The Sign of the Quotient of Two Real Numbers
 Rule 1: The Quotient of two numbers with like signs is a
positive number
(-) ÷ (-) = +
(+) ÷ (+) = +

Rule 2: The Quotient of two numbers with unlike signs is a
negative number
(+) ÷ (-) = (-) ÷ (+) = -
Divide Numbers
 Example # 52 pg 66:
18 2

 2
9
1
 Example # 54 pg 66:
30 5

 5
6 1
Example # 50 pg 66:
25 ÷ 5 or 25 5
5

1
5
Example # 53 pg 66:
36 4

4
9 1
Divide Numbers
 Example # 50 pg 66:
-12.37 ÷ 3.2
or
 12.37
 3.865
3.2
round to two decimal places
 3.87
Divide Numbers
 Example:
 36  9

 9
4
1
Example :
 53.4
 15.705
 3.4
 Example:
round to two decimals 15.71
 45  5

5
9
1
Divide Numbers
 Example # 80 pg 66:
3
16 5  16  9  (16)( 9 ) (16)(3) 48
3




or 9
  
3
9  3  5 
(1)(5)
5
5
( 3 )(5)
1
 Remember:
a a
a


b b
b
 We should write all fractions with the negative in
front

a
b
, this will be the class standard
Divide Numbers
 Example:
4  8  4  35   1  7  7
7

  

   

5 35  5   8   1   2   2
2
 Example:
 2  1   2  2   4 4



  
7
2  7   1   7 7
Summary of Operation of Real Numbers
 Page 64 Summarizes of Operation of Real Numbers
 Addition
 Subtraction
 Multiplication
 Division
 This is a good chart to use as a study guide for a test.
Evaluate Divisions Involving 0
 Zero Divided by a Nonzero Number
 If a represents any real number except 0, then
0
0a   0 , a  0
a
 Examples:
6
 2 because 3• 2  6
3
0
 0 because 1• 0  0
1
0
0
6
because (6)(0)  0
Evaluate Divisions Involving 0
 Division by Zero
 If a represents any real number except 0, then
a
a 0 
is undefined
0
 Examples:
1
 undefined
0
cannot multiple 0 by a number and get that number.
0
 can not be determined, no answer
0
2
 undefined
0
HOMEWORK 1.8
 Page 66 - 67
17, 19, 26, 29, 33, 35, 43, 45, 51, 62, 63, 67, 95