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) =  (-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 ▫ -3 4 =  -1 ∙ (3*3*3*3) =  -81 ▫ (-3) 4  (-3)(-3)(-3)(-3) =  81

Ex. 4 cont. Your Practice ▫ -5 2 (-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