1. Do Now Evaluate each expression. 1. 17 · 52. 8 · 34 3. 4 · 864. 20 · 850 5. 275 ÷ 56. 112 ÷ 4 85 272 344 Course 2 2-4 Multiplying and Dividing Integers 17,000 55 28 Hwk: p 16

2. EQ: How do I multiply and divide integers? Course 2 2-4 Multiplying and Dividing Integers M7N1c. Add, subtract, multiply, and divide positive and negative rational numbers.

3. Course 2 2-4 Multiplying and Dividing Integers MULTIPLYING AND DIVIDING INTEGERS If the signs are:Your answer will be: the same different positive negative X /+- ++- --+

4. Use a number line to find each product. Additional Example 1A: Multiplying Integers Using Repeated Addition Course 2 2-4 Multiplying and Dividing Integers –7 · 2 + (–7) + (–7) –7 · 2 = 2 · (-7) -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 –7 · 2 = –14

5. Use a number line to find each product. Additional Example 1B: Multiplying Integers Using Repeated Addition Course 2 2-4 Multiplying and Dividing Integers –8 · 3 –8 · 3 = 3 · (–8) – 8 · 3 = –24 + (–8) + (–8) + (–8) –24–23–22–21–20–19–18–17-16-15-14-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

6. Use a number line to find each product. Check It Out: Example 1A Course 2 2-4 Multiplying and Dividing Integers –3 · 2 + (–3) + (–3) –3 · 2 = 2 · (-3) -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 –3 · 2 = –6

7. Use a number line to find each product. Check It Out: Example 1B Course 2 2-4 Multiplying and Dividing Integers –5 · 3 –5 · 3 = 3 · (–5) – 5 · 3 = –15 + (–5) + (–5) + (–5) -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

8. Course 2 2-4 Multiplying and Dividing Integers Multiplication and division are inverse operations. They “undo” each other. Notice how these operations undo each other in the patterns shown. Remember!

9. Course 2 2-4 Multiplying and Dividing Integers The patterns below suggest that when the signs of integers are different, their product or quotient is negative. The patterns also suggest that the product or quotient of two negative integers is positive.

10. Find each product. Additional Example 2: Multiplying Integers Course 2 2-4 Multiplying and Dividing Integers A. –6 · (–5) –6 · (–5) 30 B. –4 · 7 –4 · 7 -28

11. Find each product. Check It Out: Example 2 Course 2 2-4 Multiplying and Dividing Integers A. –2 · (–8) –2 · (–8) 16 B. –3 · 5 –3 · 5 –15

12. Find each quotient. Additional Example 3: Dividing Integers Course 2 2-4 Multiplying and Dividing Integers A. 35 ÷ (–5) 35 ÷ (5) –7 B. –32 ÷ (–8) 32 ÷ (–8) 4

13. Additional Example 3: Dividing Integers Course 2 2-4 Multiplying and Dividing Integers Find the quotient. C. –48 ÷ 6 –48 ÷ 6 8

14. Check It Out: Example 3 Insert Lesson Title Here Course 2 2-4 Multiplying and Dividing Integers Find each quotient. A. –12 ÷ 3 –12 ÷ 3 –4 B. 45 ÷ (–9) 45 ÷ (–9) –5

15. Check It Out: Example 3 Insert Lesson Title Here Course 2 2-4 Multiplying and Dividing Integers Find the quotient. C. –25 ÷ (–5) –25 ÷ –5 5

16. Course 3 1-6 Multiplying and Dividing Integers Additional Example 2: Using the Order of Operations with Integers A. 3(–6 – 12) = –54 = 3(–18) Simplify. B. –5(–5 + 2) = 15 = –5(–3)

17. Course 3 1-6 Multiplying and Dividing Integers Additional Example 2: Using the Order of Operations with Integers C. –2(14 – 5) = –18 = –2(9) Simplify.

18. Course 3 1-6 Multiplying and Dividing Integers Check It Out: Example 2 A. 2(1 – 8) = –14 = 2(–7) Simplify. B. 4(–3 – 8) = –44 = 4(–11)

19. Course 3 1-6 Multiplying and Dividing Integers Check It Out: Example 2 C. –3(6 – 9) = 9 = –3(–3) Simplify.

20. Mrs. Johnson kept track of a stock she was considering buying. She recorded the price change each day. What was the average change per day? Additional Example 4: Averaging Integers Course 2 2-4 Multiplying and Dividing Integers Day MonTueWedThuFri Price Change ($)–$1$3$2–$5$6 (–1) + 3 + 2 + (–5) + 6 = 5 5 ÷ 5 = 1 The average change was $1 per day.

21. Check It Out: Example 4 Insert Lesson Title Here Course 2 2-4 Multiplying and Dividing Integers Mr. Reid kept track of his blood sugar daily. He recorded the change each day. What was the average change per day? (–8) + 2 + 4 + (–9) + 6 = –5 –5 ÷ 5 = –1 The average change per day was –1 unit. Day MonTueWedThuFri Unit Change –824–96

22. TOTD Use a number line to find the product. 1. –8 · 2 Find each product or quotient. 2. –3 · 5 · (–2) 3. –75 ÷ 5 4. –110 ÷ (–2) –16 Insert Lesson Title Here –15 55 Course 2 2-4 Multiplying and Dividing Integers 30

23. TOTD 5. The temperature at Bar Harbor, Maine, was –3°F. It then dropped during the night to be 4 times as cold. What was the temperature then? Insert Lesson Title Here Course 2 2-4 Multiplying and Dividing Integers –12°F