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Understanding Integer Multiplication and Expression Simplification

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This lesson covers the multiplication of integers, focusing on both different and same signs, and how to simplify algebraic expressions. It includes worked examples that demonstrate the principles of multiplying integers and evaluating algebraic expressions. Key concepts include understanding products with differing signs, utilizing properties of multiplication, and step-by-step approaches to evaluate expressions. Engage with practical exercises to reinforce learning about integer operations and algebraic simplification.

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Understanding Integer Multiplication and Expression Simplification

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  1. A B C D Find 9 – (–1). A. 8 B. 9 C. 10 D. 11 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 5-Minute Check 1

  2. Splash Screen

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

  4. Concept

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

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

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

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

  9. Concept

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

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

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

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

  14. Multiply Integers with Different Signs SKI LIFTSA 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. Plan The 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. Solve 7(–450) = –3150 feet The product is negative. Example 3

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

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

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

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

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

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

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

  22. Evaluate Algebraic Expressions Evaluate –3xy if x = –4 and y = 9. –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. = 108 The product of 12 and 9 is positive. Answer: 108 Example 6

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

  24. End of the Lesson

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