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Learn the rules, properties, and practices of multiplying and dividing real numbers with positive and negative values. Practice simplifying expressions using the order of operations. Explore properties like the Multiplicative Inverse and solve math equations step by step.
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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.
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 + - = - - + = - + - = - - + = -
Math Dog(Multiply or Divide) -4 9 -4 the answer is negative +9 -36
Math Dog(Multiply or Divide) -24 -3 -3 -24 the answer is positive 8
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
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
Which property is this? 10(0) = 0 Multiplication Property of Zero
Which property is this? -1(8) = -8 Multiplication Property of Negative One
Which property is this? 23(1) = 23 Identity Property of Multiplication
–(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
(–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
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)
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
One More Property A number’s multiplicative inverse is the of that number. RECIPROCAL
Find the Multiplicative Inverse • ⅘ • -7 • ⅚ • -⅓ • 5/4 • -1/7 • 6/5 • -3
Ticket out the door (TOD) Given: a = -5, b = -2, m = -3, and p = -1 Evaluate • 6ab • (mp)3 • a + m bp
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
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.
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.
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.
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.
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.
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 .