Download 2-3 Multiplying and Dividing Rational Numbers

2-3 Multiplying and Dividing Rational
Numbers
Ex. 1 Multiplying
• Same Signs
▫ Always positive answer
 2(2) = 4 or -2(-2) = 4
• Different Signs
▫ Always a negative answer
 4(-6) = -24
• Simplify
▫ -10(-5) =
▫ 50
Ex 1. Cont.
• Your practice
▫ -2/3(3/4) =
▫ -6/12 =
▫ -1/2
Ex. 2 Evaluating
• Evaluate -2xy for x = -20 and y = -3
▫ Plug and chug
 -2(-20)(-3) =
 -120
• -2(-3)(cd) for c = -8 and d = -7
• Put parenthesis around negatives
▫ -2(-3)((-8)(-7)) =
 6(56) =
 336
Ex. 2 Cont.
• Your practice
• Evaluate
▫ 8p ∙ (-2n) for p = -1 and n = 3
 8(-1) ∙ (-2(3)) =
 -8 ∙ (-6) =
 48
Ex. 3 Story Problems
• Use the expression given and then evaluate
▫ t = -5.5(a/1000) for a = altitude
▫ a = 8000
 t = -5.5(8000/1000)
 t = -5.5(8)
 t = -44
• Your practice
▫ Quick check number 3
Ex. 4 Simplifying Exponents
• Use PEMDAS
• Simplify
▫ -34 =
 -1 ∙ (3*3*3*3) =
 -81
▫ (-3)4
 (-3)(-3)(-3)(-3) =
 81
Ex. 4 cont.
• Your Practice
▫ -52(-3)3 =
 -1(5*5) ∙ (-27) =
 -25 ∙ (-27) =
 625
Ex. 5 Dividing
• Same signs
▫ Always a positive answer
 (-20)/(-10) = 2 or (20)/(10) = 2
• Different signs
▫ Always a negative answer
 (-20)/(10) = -2 or (20)/(-10) = -2
• Simplify
▫ (3-14)/2 =
 (-11)/2 = -11/2 or -5 1/2
• Your practice
▫ -56/(4+3) =
 -56/7 =
 -8
Ex. 6 Evaluating
• Evaluate –x/(-4) + 2y ÷ z for x = -20, y = 6, and z = -1
▫ -(-20)/(-4) + 2(6) ÷ (-1) =
 20/(-4) +12 ÷ (-1) =
 -5 + (-12) =
 -17
• Your practice
• Evaluate (2z + x)/(2y) for x = 8, y = -5, and z = -3
▫ (2(-3) + 8)/(2(-5))
 (-6 + 8)/(-10)
 2/-10
 -1/5
Ex. 7 Division Using Reciprocal
• x/y is x ÷ y
▫ (-3/4)/(-5/2) is (-3/4) ÷ (-5/2)
• K eep C hange F lip
▫ (-3/4) ∙ (-2/5) – Multiply straight across
▫ (6/20) =
▫ 3/10
• Your practice
▫ -3m/t for m = 5/6 and t = 1/6





-3(5/6) ÷ 1/6 =
-15/6 ÷ 1/6 =
-15/6 ∙ 6/1 =
-90/6 =
-15