1. Holt CA Course 1 2-4 Multiplying and Dividing Integers NS2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Also covered: AF1.4 California Standards

2. Holt CA Course 1 2-4 Multiplying and Dividing Integers VOCABULARY CARDS Multiplying and Dividing Integers

3. Holt CA Course 1 2-4 Multiplying and Dividing Integers You can think of multiplication as repeated addition. 3  2 = 2 + 2 + 2 = 6 and 3  (–2) = (–2) + (–2) + (–2) = –6

4. Holt CA Course 1 2-4 Multiplying and Dividing Integers Inverse operations “undo” each other. Multiplying by a number is the inverse operation of dividing by that number. Remember!

5. Holt CA Course 1 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.

6. Holt CA Course 1 2-4 Multiplying and Dividing Integers MULTIPLYING AND DIVIDING INTEGERS # Negative signs are: Your answer: positive negative

7. Holt CA Course 1 2-4 Multiplying and Dividing Integers Find each product. Example 1: Multiplying Integers 1A. –6  (–5) –6  (–5) Both signs are negative, so the product is positive. 30 1B. –4  7 –4  7 The signs are different, so the product is negative. –28

8. Holt CA Course 1 2-4 Multiplying and Dividing Integers Find each product. Practice 1: 1A. –2  (– 8) –2  (–8) Both signs are negative, so the product is positive. 16 1B. –3  5 –3  5 The signs are different, so the product is negative. –15

9. Holt CA Course 1 2-4 Multiplying and Dividing Integers Find each quotient. Example 2: Dividing Integers 2A. 35 ÷ (–5) 35 ÷ (5) –7 2B. –48 ÷ 6 –48 ÷ (6) –8 The signs are different, so the quotient is negative. The signs are different, so the quotient is negative.

10. Holt CA Course 1 2-4 Multiplying and Dividing Integers Practice 2: Find each quotient. 2A. –12 ÷ 3 –12 ÷ 3 –4 The signs are different, so the quotient is negative. 2B. –25 ÷ (–5) –25 ÷ –5 5 The signs are the same, so the quotient is positive.

11. Holt CA Course 1 2-4 Multiplying and Dividing Integers At 7:00, the temperature was 14ºF. As a cold front approached, the temperature dropped 6ºF per hour over the next 4 hours. What was the temperature at 11:00? Example 3: Weather Application 14 – 6  4 Multiply 6 by 4 to find the total number of degrees; then subtract it from the original temperature of 14 º F. 14 – 24 Subtract the total number of degrees to find out what the temperature was at 11:00. Use the order of operations. Multiply first. Then subtract. –10 The temperature at 11:00 was –10F.

12. Holt CA Course 1 2-4 Multiplying and Dividing Integers At 4:00, the train was 20 miles from the station. The train traveled 18 miles away from the station per hour over the next 6 hours. How far was the train from the station at 10:00? Practice 3: 20 + 18  6 Multiply 18 by 6 to find the total number of miles; then add it to the original distance of 20 miles. 20  108 Add the total number of miles from the train station to find out how far the train was at 10:00. Use the order of operations. Multiply first. Then add. 128 The train was 128 miles from the station at 10:00.

13. Holt CA Course 1 2-4 Multiplying and Dividing Integers Lesson Quiz Use a number line to find the product. 1. –8  2 Find each product or quotient. 2. –3  5  (–2)3. –75 ÷ 54. –110 ÷ (–2) –16 –155530 5. The temperature in Bar Harbor, Maine, was –3°F. It then dropped 3 degrees per hour over the next 3 hours. What was the temperature then? –12°F