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2-3 Multiplying and Dividing Rational Numbers

2-3 Multiplying and Dividing Rational Numbers

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2-3 Multiplying and Dividing Rational Numbers

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  1. 2-3 Multiplying and Dividing Rational Numbers

  2. 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

  3. Ex 1. Cont. • Your practice • -2/3(3/4) = • -6/12 = • -1/2

  4. 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

  5. Ex. 2 Cont. • Your practice • Evaluate • 8p ∙ (-2n) for p = -1 and n = 3 • 8(-1) ∙ (-2(3)) = • -8 ∙ (-6) = • 48

  6. 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

  7. Ex. 4 Simplifying Exponents • Use PEMDAS • Simplify • -34 = • -1 ∙ (3*3*3*3) = • -81 • (-3)4 • (-3)(-3)(-3)(-3) = • 81

  8. Ex. 4 cont. • Your Practice • -52(-3)3 = • -1(5*5) ∙ (-27) = • -25 ∙ (-27) = • 625

  9. 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

  10. 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

  11. Ex. 7 Division Using Reciprocal • x/y is x ÷ y • (-3/4)/(-5/2) is (-3/4) ÷ (-5/2) • K eepC hangeF 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