1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up
Simplify each expression.
1. 17   34
3. 4   850
÷ ÷ 4 85
272
344
17,000 55 28

3. 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

4. You can think of multiplication as repeated addition.
3  2 = = 6 and
3  (–2) = (–2) + (–2) + (–2) = –6

5. Additional Example 1A: Multiplying Integers Using Repeated Addition
Use a number line to find the product.
–7  2
Use the Commutative Property.
–7  2 = 2  (–7)
Think: Start at 0.
Add –7 two times.
+ (–7) (–7)
–7  2 = –14

6. Additional Example 1B: Multiplying Integers Using Repeated Addition
Use a number line to find the product.
Use the Commutative Property.
–8  3
–8  3 = 3  (–8)
Think: Start at 0.
Add –8 three times.
+ (–8) (–8) (–8)
–24–23–22–21–20–19–18–
–8  3 = –24

7. Use a number line to find the product.
Check It Out! Example 1A
Use a number line to find the product.
Think: Start at 0.
Add –3 two times.
2  (–3)
+ (–3) (–3)
2  (–3) = –6

8. Use a number line to find the product.
Check It Out! Example 1B
Use a number line to find the product.
Use the Commutative Property.
–5  3
–5  3 = 3  (–5)
Think: Start at 0.
Add –5 three times.
+ (–5) (–5) (–5)
–5  3 = –15

9. Inverse operations “undo” each other
Inverse operations “undo” each other. Multiplying by a number is the inverse operation of dividing by that number.
Remember!

10. 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.

11. MULTIPLYING AND DIVIDING INTEGERS
If the signs are:
Your answer will be:
the same
positive
different
negative

12. Additional Example 2: Multiplying Integers
Find each product.
A. –6  (–5)
–6  (–5)
Both signs are negative, so
the product is positive. 30
B. –4  7
–4  7
The signs are different, so
the product is negative.
–28

13. Check It Out! Example 2
Find each product.
A. –2  (–8)
–2  (–8)
Both signs are negative, so
the product is positive. 16
B. –3  5
–3  5
The signs are different, so
the product is negative.
–15

14. Additional Example 3: Dividing Integers
Find each quotient.
A. 35 ÷ (–5)
The signs are different, so the
quotient is negative.
35 ÷ (-5) –7
B. –48 ÷ 6
The signs are different, so the quotient is negative.
–48 ÷ (6) –8

15. Check It Out! Example 3
Find each quotient.
A. –12 ÷ 3
–12 ÷ 3
The signs are different, so the
quotient is negative. –4
B. –25 ÷ (–5)
The signs are the same, so the
quotient is positive.
–25 ÷ –5 5

16. Additional Example 4: Weather Application
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?
Subtract the total number of degrees to find out what the temperature was at 11:00.
14 – 6  4
Multiply 6 by 4 to find the total number of degrees; then subtract it from the original temperature of 14ºF.
Use the order of operations. Multiply first. Then subtract.
14 – 24
–10
The temperature at 11:00 was –10F.

17. Use the order of operations. Multiply first. Then add. 20 + 108
Check It Out! Example 4
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?
Add the total number of miles from the train station to find out how far the train was at 10:00.
 6
Multiply 18 by 6 to find the total number of miles; then add it to the original distance of 20 miles.
Use the order of operations. Multiply first. Then add.
The train was 128 miles from the station at 10:00.
128

18. Lesson Quiz
Use a number line to find the product.
1. –8  2
Find each product or quotient.
2. –3  5  (–2) 3. –75 ÷ –110 ÷ (–2)
–16 30
–15 55
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