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For use with pages xxx–xxx

3. A climber is 10400 ft above sea level. He descends 500 ft to a fellow climber. What is his new height above sea level?. –. ANSWER. ANSWER. –. 11.1. –. 38. 9900 ft. ANSWER. ANSWER. 32.7. 9/12/12 Warm-Up. For use with pages xxx–xxx. 4. Find. 1. ?. –. 21. 17. –. –. 17.3.

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For use with pages xxx–xxx

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  1. 3. A climber is 10400 ft above sea level. He descends 500 ft to a fellow climber. What is his new height above sea level? – ANSWER ANSWER – 11.1 – 38 9900 ft ANSWER ANSWER 32.7 9/12/12 Warm-Up For use with pages xxx–xxx 4. Find 1. ? – 21 17 – – 17.3 + 6.2 = 2. ? ) 26.9 – ( – 5.8 = 11.8 ANSWER 5.

  2. The Rules of Multiplying and Dividing Real Numbers • Two numbers that are multiplied or divided with the SAME SIGN give a POSITIVE answer +  + = + -  - = + +  + = + -  - = + • Two numbers that are multiplied or divided with DIFFERENT SIGNS give a NEGATIVE answer +  - = - -  + = - +  - = - -  + = -

  3. Math Dog(Multiply or Divide)

  4. Math Dog(Multiply or Divide) -4  9 -4 the answer is negative +9 -36

  5. Math Dog(Multiply or Divide) -24  -3 -3 -24 the answer is positive 8

  6. The product of two negative numbers is positive. –3(–11) = 33 –6() = – The product of a positive number and a negative number is negative. 3 4 18 4 Multiplying and Dividing Real Numbers LESSON 1-6 Additional Examples Simplify each expression. a. –3(–11) 3 4 b. –6( ) = _ 9 2

  7. Multiplying and Dividing Real Numbers Practice LESSON 1-6 Additional Examples Simplify each expression. (choose 4) • -8(3) • 4(-4) • -20(-6 + 2) • -7(-1.2) • -11(⅛) • 15(-⅗) • | (-12)2 | • | (-10)(-5) | Answers • -24 • -16 • 80 • 8.4 • -11/8 • -9 • 24 • 50

  8. Properties of Multiplication

  9. Which property is this? 10(0) = 0 Multiplication Property of Zero

  10. Which property is this? -1(8) = -8 Multiplication Property of Negative One

  11. Which property is this? 23(1) = 23 Identity Property of Multiplication

  12. –(0.2 • 0.2 • 0.2 • 0.2) Write as repeated multiplication. = = –0.0016 Simplify. (–0.2)(–0.2)(–0.2)(–0.2) Write as repeated multiplication. = = 0.0016 Simplify. Multiplying and Dividing Real Numbers LESSON 1-6 Additional Examples Use the order of operations to simplify each expression. I DO a. –0.24 WE DO b. (–0.2)4

  13. (–0.3)(–0.3)(–0.3) = Multiplying and Dividing Real Numbers LESSON 1-6 Additional Examples Use the order of operations to simplify each expression. YOU DO TOGETHER a. (–0.3)3 = –0.027 b. –0.33 –(0.3 • 0.3 • 0.3) = -0.027

  14. The quotient of a positive number and a negative number is negative. = –20 The quotient of a negative number and a negative number is positive. = 6 Multiplying and Dividing Real Numbers LESSON 1-6 Additional Examples Simplify each expression. a. 100 ÷ (–5) b. –54 ÷ (–9)

  15. Multiplying and Dividing Real Numbers Practice LESSON 1-6 Additional Examples Simplify each expression. (choose 3) • -24 ÷(- 4) • 36 ÷ (-3) • -16 ÷ (-6 + 2) • -1÷ (0.2) • - 23 ÷ (3) • 15 ÷ (8 – 11) Answers • 6 • -12 • 4 • -5 • -23/3 or -7⅔ • -5

  16. One More Property A number’s multiplicative inverse is the of that number. RECIPROCAL

  17. Find the Multiplicative Inverse • ⅘ • -7 • ⅚ • -⅓ • 5/4 • -1/7 • 6/5 • -3

  18. Ticket out the door (TOD) Given: a = -5, b = -2, m = -3, and p = -1 Evaluate • 6ab • (mp)3 • a + m bp

  19. 9/13/12 Warm Up Simplify • -13(4) • -8(-9 + 2) • 72 ÷ (-12) • -102÷ (-2) • (2 – 3)(7)(-6 + 9) • What is another word for multiplicative inverse? Answers • -52 • 56 • -6 • 50 • -21 • .reciprocal

  20. Multiplying and Dividing Real Numbers LESSON 1-6 Additional Examples Evaluate 5rs for r = –18 and s = –5. 5rs = 5(–18)(–5) Substitute –18 for r and –5 for s. = –90(–5) 5(–18) results in a negative number, –90. = 450 –90(–5) results in a positive number, 450.

  21. Multiplying and Dividing Real Numbers LESSON 1-6 Additional Examples Evaluate -3ab for a = –7 and s = 9. 5rs = 5(–18)(–5) Substitute –18 for r and –5 for s. = –90(–5) 5(–18) results in a negative number, –90. = 450 –90(–5) results in a positive number, 450.

  22. Practice

  23. a 1000 7200 1000 –5.5( ) = –5.5 ( ) Substitute 7200 for a. Multiplying and Dividing Real Numbers LESSON 1-6 Additional Examples a 1000 Use the expression –5.5( ) to calculate the change in temperature for an increase in altitude a of 7200 ft. = –5.5(7.2) Divide within parentheses. = –39.6°F Multiply. The change in temperature is –39.6°F.

  24. x y x y – – 4z2 = – 4(–4)2Substitute 4 for x, –2 for y, and –4 for z. –4 –2 –4 –2 = – 4(16) Simplify the power. Multiplying and Dividing Real Numbers LESSON 1-6 Additional Examples Evaluate – – 4z2 for x = 4, y = –2, and z = –4. = 2 – 64 Divide and multiply. = –62 Subtract.

  25. 3 2 3 4 p r = p ÷ rRewrite the equation. 3 2 3 4 3 2 (– ) 3 4 = ÷Substitute for p and – for r. 3 2 3 4 4 3 4 3 (– ) = Multiply by – , the reciprocal of – . Multiplying and Dividing Real Numbers LESSON 1-6 Additional Examples p r Evaluate for p = and r = – . = –2 Simplify.

  26. Practice

  27. 1 2 3 Multiplying and Dividing Real Numbers LESSON 1-6 Lesson Quiz • Simplify. • –8(–7) 2. –6(–7 + 10) – 4 • Evaluate each expression for m = –3, n = 4, and p = –1. • 3. + p 4. (mp)35.mnp • 6. Evaluate 2a ÷ 4b – c for a = –2, b = – , and c = – – 22 56 8m n –7 27 12 1 2 1 3 .

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