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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 (-) · (-) = + (+) · (+) = +

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Mth 11203 algebra

MTH 11203Algebra

Multiplication and division of Real Numbers

CHAPTER 1 Section 8


Multiply numbers
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 numbers1
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 pos. because same signs

  • Example: (6)(-9) = -54 neg. because different signs


Multiply numbers2
Multiply Numbers

  • Example: (-8)(-4) = 32 pos. because same signs

  • Example: (0)(-8) = 0 0 is never pos. or neg.

  • Example: (-4)(-6) = 24 pos. because same signs

  • Careful not to confuse subtraction with multiplication

    Example -4 – 5 (-4)(-5)

    -4 + (-5) 20

    -9


Multiply numbers3
Multiply Numbers

  • Example

  • Example

  • Remember that negatives can be written different ways


Multiply numbers4
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) Odd negatives equals negative results

    (-8)(-1)(-5)

    (8)(-5)

    -40


Multiply numbers5
Multiply Numbers

  • Example :

    (-3)(2)(-1)(-2)(-4) Even negatives equals (-6)(-1)(-2)(-4) positive results

    (6)(-2)(-4)

    (-12)(-4)

    48

  • Example :

    (-3)(4)(-9)(-3) Odd negatives equals (-12)(-9)(-3) Negative results

    (108)(-3)

    -324


Multiply numbers6
Multiply Numbers

  • Example :

    (-2)(4)(-1)(-3)(-5) Even negatives equals (-8)(-1)(-3)(-5) positive results

    (8)(-3)(-5)

    (-24)(-5)

    120


Divide numbers
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 numbers1
Divide Numbers

  • Example # 52 pg 66: Example # 50 pg 66:

    25 ÷ 5 or

  • Example # 54 pg 66: Example # 53 pg 66:


Divide numbers2
Divide Numbers

  • Example # 50 pg 66:

    -12.37 ÷ 3.2 or


Divide numbers3
Divide Numbers

  • Example: Example :

  • Example:


Divide numbers4
Divide Numbers

  • Example # 80 pg 66:

  • Remember:

  • We should write all fractions with the negative in front , this will be the class standard


Divide numbers5
Divide Numbers

  • Example:

  • Example:


Summary of operation of real numbers
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
Evaluate Divisions Involving 0

  • Zero Divided by a Nonzero Number

    • If a represents any real number except 0, then

  • Examples:


Evaluate divisions involving 01
Evaluate Divisions Involving 0

  • Division by Zero

    • If a represents any real number except 0, then

  • Examples:


Homework 1 8
HOMEWORK 1.8

  • Page 66 - 67

    17, 19, 26, 29, 33, 35, 43, 45, 51, 62, 63, 67, 95


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