1. 11-7 Multiplying Integers Warm Up Find each product. 1. 8 42. 7 12 3. 3 94. 6 5 5. 80 66. 50 6 7. 40 908. 20 700 32 84 27 30 480 300 3,600 14,000

2. 11-7 Multiplying Integers Learn to multiply integers.

3. 11-7 Multiplying Integers –66Product –(2 + 2 + 2) ‏ 2 + 2 + 2Addition the opposite of 3 groups of 2 Words –3 23 2Numbers

4. 11-7 Multiplying Integers 6–6Product –[(–2) + (–2) + (–2)](–2) + (–2) + (–2) ‏ Addition the opposite of 3 groups of –2 Words –3 (–2) ‏ 3 (–2) ‏ Numbers

5. 11-7 Multiplying Integers Additional Example 1: Multiplying Integers Find each product. A. 5 2 B. 4 (–5) ‏ 5 2 = 10Think: 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!

6. 11-7 Multiplying Integers 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.

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

8. 11-7 Multiplying Integers 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.

9. 11-7 Multiplying Integers MULTIPLYING INTEGERS 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

10. 11-7 Multiplying Integers Additional Example 2: Evaluating Integer Expressions Evaluate –7x for each value of x. A. x = –3 B. x = 5 –7xWrite the expression. –7 (–3) ‏ Substitute –3 for x. 21 The signs are the same, so the answer is positive. –7xWrite the expression. –7 5Substitute 5 for x. –35The signs are different, so the answer is negative. –7x means –7 x. Remember!

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

12. 11-7 Multiplying Integers Learn to divide integers.

13. 11-7 Multiplying Integers Multiplication and division are inverse operations. To solve a division problem, think of the related multiplication. To find the mean of a list of numbers: 1. Add all the numbers together. 2. Divide by how many numbers are in the list. Remember!

14. 11-7 Multiplying Integers 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.

15. 11-7 Multiplying Integers Check It Out: Example 1 Find each quotient. A. –15 ÷ 5 B. –36 ÷ (–6) ‏ Think: What number times 5 equals –15? –3 5 = –15, so –15 ÷ 5 = –3. Think: What number times –6 equals –36? 6 (–6) = –36, so –36 ÷ (–6) = 6.

16. 11-7 Multiplying Integers Dividing 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 0 14 __ 0 –11 __ You cannot divide any integer by 0. Because division is the inverse of multiplication, the rules for dividing integers are the same as the rules for multiplying integers.

17. 11-7 Multiplying Integers Additional Example 2A: Evaluating Integer Expressions Evaluate for each value of d. d = 16 Write the expression. = 16 ÷ 4 Substitute 16 for d. = 4 The signs are the same, so the answer is positive. d 4 __ d 4 16 4 __

18. 11-7 Multiplying Integers Additional Example 2B: Evaluating Integer Expressions Evaluate for each value of d. d = –24 Write the expression. = –24 ÷ 4 Substitute –24 for d. = –6 The signs are different, so the answer is negative. d 4 __ d 4 -24 4 ___

19. 11-7 Multiplying Integers Additional Example 2C: Evaluating Integer Expressions Evaluate for each value of d. d = –12 Write the expression. = –12 ÷ 4 Substitute –12 for d. = –3 The signs are different, so the answer is negative. d 4 __ d 4 -12 4 ___