Multiplication and division of Real Numbers CHAPTER 1 Section 8 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 # 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 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 (-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

Divide Numbers Example # 50 pg 66: -12.37 ÷ 3.2 or

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:

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:

HOMEWORK 1.8 Page 66 - 67 17, 19, 26, 29, 33, 35, 43, 45, 51, 62, 63, 67, 95