11-6

1. 11-6 Multiplying & Dividing Integers Course 1 Warm Up Problem of the Day Lesson Presentation

2. Multiplying Integers 11-6 Course 1 Warm Up Find each product. 1.8 • 4 2. 7•12 3. 3 • 9 4. 6 • 5 5. 80 • 6 6. 50 • 6 7. 40 • 90 8. 20 • 700 84 32 30 27 480 300 3,600 14,000

3. Notes on Multiplying and Dividing Integers • Steps • Multiply and Divide as usual. • When there is an even amount of negative signs, the final answer is positive. • When there is an odd amount of negative signs, the final answer is negative.

4. Examples

5. Multiplying Integers 11-6 Course 1

6. Multiplying Integers 11-6 Course 1

7. Dividing Integers 11-7 0 0 __ __ 14 –11 Course 1 Because division is the inverse of multiplication, the rules for dividing integers are the same as the rules for multiplying integers. If the signs are the same, the product is positive. 24 ÷ 3 = 8 –6 ÷ (–3) = 2 If the signs are different, the quotient is negative. –20 ÷ 5 = –4 72 ÷ (–8) = –9 Zero divided by any integer equals 0. = 0 = 0 You cannot divide any integer by 0.

8. Multiplying Integers 11-6 Remember! To find the opposite of a number, change the sign. The opposite of 6 is –6. The opposite of –4 is 4. Course 1 Additional Example 1: Multiplying Integers Find each product. A. 5 • 2 B. 4 • (–5) 5 • 2 = 10 Think: 5 groups of 2. Think: 4 groups of –5. 4 • (–5) = –20

9. Multiplying Integers 11-6 Course 1 Additional Example 1: Multiplying Integers Find each product. C. –3 • 2 D.–2•(–4) Think: the opposite of 3 groups of 2. –3 • 2 = –6 Think: the opposite of 2 groups of –4. –2 • (–4) = 8

10. Multiplying Integers 11-6 Course 1 Check It Out: Example 1 Find each product. A. 3 • 4 B. 2 • (–7) 3 • 4 = 12 Think: 3 groups of 4. Think: 2 groups of –7. 2 • (–7) = –14

11. Multiplying Integers 11-6 Course 1 Check It Out: Example 1 Find each product. C. –5 • 3 D.–4•(–6) Think: the opposite of 5 groups of 3. –5 • 3 = –15 Think: the opposite of 4 groups of –6. –4 • (–6) = 24

12. Multiplying Integers 11-6 Course 1 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

13. Dividing Integers 11-7 Course 1 Additional Example 1: Dividing Integers Find each quotient. A. –30 ÷ 6 B. –42 ÷ (–7) Think: What number times 6 equals –30? –5 • 6 = –30, so –30 ÷ 6 = –5. Think: What number times –7 equals –42? 6 • (–7) = –42, so –42 ÷ (–7) = 6.

14. Multiplying Integers 11-6 Remember! –7x means –7 •x. Course 1 Additional Example 2: Evaluating Integer Expressions Evaluate –7x for each value of x. A. x = –3 B. x = 5 –7x Write the expression. –7 •(–3) Substitute –3 for x. The signs are the same, so the answer is positive. 21 –7x Write the expression. –7 •5 Substitute 5 for x. –35 The signs are different, so the answer is negative.

15. Multiplying Integers 11-6 Course 1 Check It Out: Example 2 Evaluate –4y for each value of y. A. y = – 2 B. y = 7 –4y Write the expression. –4 •(–2) Substitute –2 for y. 8 The signs are the same, so the answer is positive. –4y Write the expression. –4 •7 Substitute 7 for y. –28 The signs are different, so the answer is negative.

16. Multiplying Integers 11-6 Course 1 Insert Lesson Title Here Lesson Quiz Find each product. 1. 6 • (4) 2. 3 • (–2) 3. –9 • (–2) 4. –6 • 5 5. Evaluate 3y 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? 24 –6 –30 18 –21 –2