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# MTH 11203 Algebra - PowerPoint PPT Presentation

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 11203Algebra

Multiplication and division of Real Numbers

CHAPTER 1 Section 8

• 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.

• 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

• 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

• Example

• Example

• Remember that negatives can be written different ways

• Multiplication of more that one number in a given problem:

• 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

• 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

• Example :

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

(8)(-3)(-5)

(-24)(-5)

120

• 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

(+) ÷ (-) = -

(-) ÷ (+) = -

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

25 ÷ 5 or

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

• Example # 50 pg 66:

-12.37 ÷ 3.2 or

• Example: Example :

• Example:

• Example # 80 pg 66:

• Remember:

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

• Example:

• Example:

• Page 64 Summarizes of Operation of Real Numbers

• Subtraction

• Multiplication

• Division

• This is a good chart to use as a study guide for a test.

• Zero Divided by a Nonzero Number

• If a represents any real number except 0, then

• Examples:

• Division by Zero

• If a represents any real number except 0, then

• Examples:

• Page 66 - 67

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