1. Multiplying and Dividing Integers
3-5
Multiplying and Dividing Integers
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Multiplying and Dividing Integers
Course 2
3-5
Multiplying and Dividing Integers
Warm Up
Evaluate each expression.
1. 17 · 5
2. 8 · 34
3. 4 · 86
4. 20 · 850
÷ 5
÷ 4 85
272
344
17,000 55 28

3. Multiplying and Dividing Integers
Course 2
3-5
Multiplying and Dividing Integers
Problem of the Day
To discourage guessing on a multiple choice test, a teacher assigns 5 points for a correct answer, and –2 points for an incorrect answer, and 0 points for leaving the questioned unanswered. What is the score for a student who had 22 correct answers, 15 incorrect answers, and 7 unanswered questions? 80

4. Multiplying and Dividing Integers
Course 2
3-5
Multiplying and Dividing Integers
Learn to multiply and divide integers.

5. Multiplying and Dividing Integers
Course 2
3-5
Multiplying and Dividing Integers
You can think of multiplication as repeated addition.
3 · 2 = = 6 and
3 · (–2) = (–2) + (–2) + (–2) = –6

6. Additional Example 1: Multiplying Integers Using Repeated Addition
Course 2
3-5
Multiplying and Dividing Integers
Additional Example 1: Multiplying Integers Using Repeated Addition
Find each product.
A. –7 · 2
Think: –7 · 2 = 2 · –7,
or 2 groups of –7.
–7 · 2 = (–7) + (–7)
= –14
B. –8 · 3
–8 · 3 = (–8) + (–8) + (–8)
= –24
Think: –8 · 3 = 3 · –8,
or 3 groups of –8.

7. Insert Lesson Title Here
Course 2
3-5
Multiplying and Dividing Integers
Insert Lesson Title Here
Try This: Example 1
Find each product.
A. –3 · 2
Think: –3 · 2 = 2 · –3,
or 2 groups of –3.
–3 · 2 = (–3) + (–3)
= –6
B. –5 · 3
–5 · 3 = (–5) + (–5) + (–5)
= –15
Think: –5 · 3 = 3 · –5,
or 3 groups of –5.

8. Multiplying and Dividing Integers
Course 2
3-5
Multiplying and Dividing Integers
The Commutative Property of Multiplication states that order does not matter when you multiply.
Remember!

9. Multiplying and Dividing Integers
Course 2
3-5
Multiplying and Dividing Integers
Example 1 suggests that when the signs of two numbers are different, the product is negative.
To decide what happens when both numbers are negative, look at the pattern at right. Notice that each product is 3 more than the preceding one. This pattern suggests that the product of two negative integers is positive.
–3 · (2) = –6
–3 · (1) = –3
–3 · (0) = 0
–3 · (–1) = 3
–3 · (–2) = 6

10. Additional Example 2: Multiplying Integers
Course 2
3-5
Multiplying and Dividing Integers
Additional Example 2: Multiplying Integers
Multiply.
–6 · (–5)
–6 · (–5) = 30
Both signs are negative, so
the product is positive.

11. Insert Lesson Title Here
Course 2
3-5
Multiplying and Dividing Integers
Insert Lesson Title Here
Try This: Example 2
Multiply.
–2 · (–8)
–2 · (–8) = 16
Both signs are negative, so
the product is positive.

12. Multiplying and Dividing Integers
Course 2
3-5
Multiplying and Dividing Integers
Multiplication and division are inverse operations. They “undo” each other. You can use this fact to discover the rules for division of integers.

13. Multiplying and Dividing Integers
Course 2
3-5
Multiplying and Dividing Integers
4 • (–2) = –8
–8 ÷ (–2) = 4
Same signs
Positive
–4 • (–2) = 8
8 ÷ (–2) = –4
Different signs
Negative
The rule for division is like the rule for multiplication.

14. Multiplying and Dividing Integers
Course 2
3-5
Multiplying and Dividing Integers
MULTIPLYING AND DIVIDING INTEGERS
If the signs are:
Your answer will be:
the same
positive
different
negative

15. Additional Example 3A & 3B: Dividing Integers
Course 2
3-5
Multiplying and Dividing Integers
Additional Example 3A & 3B: Dividing Integers
Find each quotient.
A. –27 ÷ 9
–27 ÷ 9
Think: 27 ÷ 9 = 3. –3
The signs are different, so the
quotient is negative.
B. 35 ÷ (–5)
35 ÷ (–5)
Think: 35 ÷ 5 = 7.
The signs are different, so the
quotient is negative. –7

16. Additional Example 3C: Dividing Integers
Course 2
3-5
Multiplying and Dividing Integers
Additional Example 3C: Dividing Integers
Find the quotient.
C. –32 ÷ (–8)
–32 ÷ –8
Think: 32 ÷ 8 = 4. 4
The signs are the same, so the
quotient is positive.

17. Insert Lesson Title Here
Course 2
3-5
Multiplying and Dividing Integers
Insert Lesson Title Here
Try This: Example 1A & 1B
Find each quotient.
A. –12 ÷ 3
–12 ÷ 3
Think: 12 ÷ 3 = 4. –4
The signs are different, so the
quotient is negative.
B. 45 ÷ (–9)
45 ÷ (–9)
Think: 45 ÷ 9 = 5.
The signs are different, so the
quotient is negative. –5

18. Insert Lesson Title Here
Course 2
3-5
Multiplying and Dividing Integers
Insert Lesson Title Here
Try This: Example 3C
Find the quotient.
C. –25 ÷ (–5)
–25 ÷ –5
Think: 25 ÷ 5 = 5. 5
The signs are the same, so the
quotient is positive.

19. Additional Example 4: Averaging Integers
Course 2
3-5
Multiplying and Dividing Integers
Additional Example 4: Averaging Integers
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?
Day
Mon
Tue
Wed
Thu
Fri
Price Change ($)
–$1 $3 $2
–$5 $6
Find the sum of the
changes in price.
(–1) (–5) + 6 = 5 5
= 1
Divide to find the
average.
The average change per day was $1.

20. Insert Lesson Title Here
Course 2
3-5
Multiplying and Dividing Integers
Insert Lesson Title Here
Try This: Example 4
Mr. Reid kept track of his blood sugar daily. He recorded the change each day. What was the average change per day?
Day
Mon
Tue
Wed
Thu
Fri
Unit Change –8 2 4 –9 6
Find the sum of the
changes in blood sugar.
(–8) (–9) + 6 = –5 –5 5
= –1
Divide to find the
average.
The average change per day was –1 unit.

21. Multiplying and Dividing Integers Insert Lesson Title Here
Course 2
3-5
Multiplying and Dividing Integers
Insert Lesson Title Here
Lesson Quiz
Find each product or quotient.
1. –8 · 12
2. –3 · 5 · (–2)
3. –75 ÷ 5
4. –110 ÷ (–2)
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?
–96 30
–15 55
–12˚F