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

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 Numbers

- Example
- Example
- Remember that negatives can be written different ways

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 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 Numbers

- Example :

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

(8)(-3)(-5)

(-24)(-5)

120

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: Example # 50 pg 66:

25 ÷ 5 or

- Example # 54 pg 66: Example # 53 pg 66:

Divide Numbers

- Example: Example :
- Example:

Divide Numbers

- Example # 80 pg 66:
- Remember:
- We should write all fractions with the negative in front , this will be the class standard

Divide Numbers

- Example:
- Example:

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
- Examples:

Evaluate Divisions Involving 0

- Division by Zero
- If a represents any real number except 0, then
- Examples:

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