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Over Lesson 2–3 A.A B.B C.C D.D 5-Minute Check 1 A.8 B.9 C.10 D.11 Find 9 – (–1). Find –3 – (–21). A.–24 B.–18 C.19 D.18 Evaluate the expression a – b if a = –7 and b = 9. A.–16 B.–2 C.2 D.16

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Splash Screen

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Then/Now You multiplied integers using algebra tiles. (Explore 2–4) Multiply integers. Simplify algebraic expressions.

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Concept

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Example 1 Multiply Integers with Different Signs A. Find 8(–9). 8(–9) = –72The factors have different signs. The product is negative. Answer: –72

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Example 1 Multiply Integers with Different Signs B. Find –9(11). Answer: –99 –9(11) = –99The factors have different signs. The product is negative.

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A.A B.B C.C D.D Example 1 A.–3 B.–46 C.48 D.–48 A. Find –4(12).

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A.A B.B C.C D.D Example 1 A.12 B.–12 C.–3 D.–8 B. Find 6(–2).

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Concept

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Example 2 Multiply Integers with the Same Sign A. Find –4(–16). Answer: 64 –4(–16) = 64The factors have the same sign. The product is positive.

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Example 2 Multiply Integers with the Same Sign B. Find –9(–6). Answer: 54 –9(–6) = 54The product is positive.

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A.A B.B C.C D.D Example 2 A.24 B.–24 C.–11 D.23 A. Find –3(–8).

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A.A B.B C.C D.D Example 2 A.–72 B.–17 C.17 D.72 B. Find –8(–9).

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Example 3 Multiply Integers with Different Signs SKI LIFTS A ski lift descends the side of a mountain at the rate of 450 feet per minute. What is the lift’s change in altitude after 7 minutes? UnderstandYou need to find how many feet the ski lift descends. PlanThe word descends means move downward, so the rate per minute is represented by –450. Multiply –450 times 7 to find the change after 7 minutes. Solve7(–450) = –3150 feetThe product is negative.

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Example 3 Multiply Integers with Different Signs Answer: So, the change in altitude is –3150 feet. Check7(–500) is –3500. –3150 is close to –3500.

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A.A B.B C.C D.D Example 3 A.–30 feet B.–11 feet C.11 feet D.30 feet ELEVATORS An elevator is descending at the rate of 5 feet per second. What is the change in altitude after 6 seconds?

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Example 4 Multiply More Than Two Integers Find 7(–11)(4). 7(–11)(4)= [7(–11)](4)Associative Property = (–77)(4)7(–11) = –77 = –308(–77)(4) = –308 Method 1 Use the Associative Property

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Example 4 Multiply More Than Two Integers Answer: –308 7(–11)(4)= 7(4)(–11) Commutative Property = 28(–11)7(4) = 28 = –30828(–11) = –308 Method 2 Use the Commutative Property

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A.A B.B C.C D.D Example 4 A.–120 B.–25 C.25 D.120 Find –3(8)(5).

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Example 5 Simplify Algebraic Expressions Simplify 8a(–5b). Answer: –40ab 8a(–5b)=(8)(a)(–5)(b) =(8 ● –5)(a ● b)Commutative Property of Multiplication =–40ab(8 ● –5) = –40, a ● b = ab

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A.A B.B C.C D.D Example 5 A.12c B.–12c C.8c D.–8c Simplify –6(2c).

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Example 6 Evaluate Algebraic Expressions Evaluate –3xy if x = –4 and y = 9. Answer: 108 –3xy=–3(–4)(9)Replace x with –4 and y with 9. =[–3(–4)](9)Associative Property of Multiplication =12(9)The product of –3 and –4 is positive. =108The product of 12 and 9 is positive.

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A.A B.B C.C D.D Example 6 A.–2mn B.–12mn C.35mn D.–35mn Simplify 5m(–7n).

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End of the Lesson

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