 # Algebra 1 (A/B) Fall 2012. 2.5 – Multiplication of Real Numbers  Objective: To multiply positive and negative numbers, including decimals and fractions.

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Algebra 1 (A/B) Fall 2012

2.5 – Multiplication of Real Numbers  Objective: To multiply positive and negative numbers, including decimals and fractions.

Multiplication Rules 1.(6)(-4)2. -4c (5d) 3.(-1)(-12)4. 12 ∙ (-3) 5.- 2 ∙ -116. (7)(-7) 7.8 ∙ (-3)(2)8. -2 ∙ -6 ∙ -4 9. (-3b)(-4b)(-2z)(-5z)(-1) Do the number of negative values affect the sign of the product? How? Same signs  “ + ” Diff. signs  “ – ” Even “-” signs  “+” Odd “-” signs  “–” -24 -20cd 12 -36 22 -49 -48 -120b 2 z 2 (+)(+) = (-)(-) = (+)(-) = (-)(+) = + + - -

Multiplying Decimals Multiplying Decimals What is the rule for multiplying decimals? Try these: Don’t forget the sign! 10. (2.4)(-3.1)11. 4.2(1.14) 12. (-5.3)(-0.04) 13. (2.93)(0.012)14. (-10)(3.56)(-2) Line up at the right and multiply as whole number, when finished, place decimal point from right for the total number of decimal digits. -7.444.7880.212 0.0351671.2

Multiplying Fractions Try these: Don’t forget the sign! 15.16.17. 18. 19. What is the rule for multiplying fractions? What should you do to make whole numbers look like fractions? To make the multiplication easier, diagonally or vertically cancel the greatest common factor between any numerator and denominator and then multiply the numerators and denominators across. Just put the denominator “1”.

Properties of Multiplication DefinitionExample Commutative a · b = b · a Associative (a· b) · c = a · (b· c) Identity a · 1 = a Zero a · 0 = 0 Opposites (-1) · a = -a 4 · (-2) = (-2) · 4 [(-4) · 3] · (-2) = (-4) · [ 3 · (-2)] (-2) · 1 = -2 (-5) · 0 = 0 (-1) · 14 = -14

Simplifying Variable Expressions  Figure out if your answer is positive or negative  Combine the same variables 20. (-4)(-z) 21. 6(-y)(-y)(-y) 22. -(-b) 2 23. (-1/2) ∙ (-2x) 24. (-3/4) ∙ (-a 2 )(4a) 4z-6y 3 -b 2 x3a 3

Multiplying Negative X Negative Positive X Positive DecimalsFractions POSITIVE! Straight Across Ignore decimals, then count numbers behind decimals to figure out where decimal goes Whole Numbers Positive X Negative Negative X Positive NEGATIVE!

Multiplication Puzzle

Partner Practice: Treasure Hunt

Homework  pg. 96 #16-40 (every other even) This means: #16, 18, 20, 22, 24, 26, 28, …

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