3. Problem of the Day Catherine has $14.00 and earns $12.00 for each lawn she mows. If she mows 4 lawns and buys 5 DVDs that cost $11.95 each, including tax, how much money does she have left? $2.25
4. Preview of MA.7.A.3.1 Use and justify the rules for…multiplying…integers. Preview of MA.7.A.3.2 …Multiply…integers,…including solving problems in everyday contexts. Sunshine State Standards
5. – 6 6 Product – (2 + 2 + 2) 2 + 2 + 2 Addition the opposite of 3 groups of 2 3 groups of 2 Words – 3 • 2 3 • 2 Numbers
6. 6 – 6 Product – [(–2) + (–2) + (–2)] (–2) + (–2) + (–2) Addition the opposite of 3 groups of –2 3 groups of –2 Words – 3 • (–2) 3 • (–2) Numbers
7. Additional Example 1: Multiplying Integers Find each product. A. 5 • 2 B. 4 • (–5) 5 • 2 = 10 Think: 5 groups of 2. 4 • (–5) = –20 Think: 4 groups of –5. To find the opposite of a number, change the sign. The opposite of 6 is –6. The opposite of –4 is 4. Remember!
8. Additional Example 1: Multiplying Integers Find each product. C. –3 • 2 D. –2 • (–4) – 3 • 2 = –6 Think: the opposite of 3 groups of 2. – 2 • (–4) = 8 Think: the opposite of 2 groups of –4.
9. Check It Out: Example 1 Find each product. A. 3 • 4 B. 2 • (–7) 3 • 4 = 12 Think: 3 groups of 4. 2 • (–7) = –14 Think: 2 groups of –7.
10. Check It Out: Example 1 Find each product. C. –5 • 3 D. –4 • (–6) – 5 • 3 = –15 Think: the opposite of 5 groups of 3. – 4 • (–6) = 24 Think: the opposite of 4 groups of –6.
11. If the signs are the same, the product is positive. 4 • 3 = 12 –6 • (–3) = 18 If the signs are different, the product is negative. – 2 • 5 = –10 7 • (–8) = –56 The product of any number and 0 is 0. 0 • 9 = 0 (–12) • 0 = 0 MULTIPLYING INTEGERS
12. Additional Example 2: Evaluating Integer Expressions Evaluate –7 x for each value of x . A. x = –3 B. x = 5 – 7 x Write the expression. – 7 • (–3) Substitute –3 for x. 21 The signs are the same, so the answer is positive. – 7 x Write the expression. – 7 • 5 Substitute 5 for x. – 35 The signs are different, so the answer is negative. – 7x means –7 • x . Remember!
13. Check It Out: Example 2 Evaluate –4 y for each value of y . A. y = – 2 B. y = 7 – 4 y Write the expression. – 4 • (–2) Substitute –2 for y. 8 The signs are the same, so the answer is positive. – 4 y Write the expression. – 4 • 7 Substitute 7 for y. – 28 The signs are different, so the answer is negative.
15. Lesson Quiz Find each product. 1. 6 • (4) 2. 3 • (–2) 3. –9 • (–2) 4. –6 • 5 5. Evaluate 3 y for y = –7. 6. During a football game, Raymond’s team lost 6 yards on each of 3 plays and gained 8 yards on each of two plays. What integer represents the total change in the team’s position? – 6 24 18 – 30 – 21 – 2
16. 1. Find the product. 4 7 A. 11 B. 28 C. 47 D. –3 Lesson Quiz for Student Response Systems
17. 2. Find the product. 2 (–9) A. –7 B. 18 C. –18 D. 7 Lesson Quiz for Student Response Systems
18. 3. Find the product. –13 (–4) A. –17 B. –52 C. 52 D. 17 Lesson Quiz for Student Response Systems
19. 4. Evaluate 6 m for m = –8. A. –2 B. –14 C. –48 D. –68 Lesson Quiz for Student Response Systems
20. 5. On a quiz, Ronald got 5 points each for 4 correct answers and lost 3 points each for 8 incorrect answers. Which integer represents the total points earned by Ronald? A. 4 B. –4 C. 44 D. –44 Lesson Quiz for Student Response Systems
