The document focuses on multiplying and dividing integers, emphasizing key concepts such as the basic operations, commutative property, and the rules for signs in products and quotients. It includes various examples and exercises to reinforce the learning, highlighting that multiplication and division are inverse operations. Additionally, it features real-world applications and problems to help students practice and understand the concepts better.

1. Multiplication and
Dividing Integers
Week 5-6

2. Warm Up
Evaluate each expression.
1. 17 · 5
2. 8 · 34
3. 4 · 86
4. 20 · 850
5. 275 ÷ 5
6. 112 ÷ 4
85
272
344
Course 2
Multiplying and Dividing Integers
17,000
55
28

3. Learn to multiply and divide integers.
Multiplying and Dividing Integers

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

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

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

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

8. Course 2
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

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

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

11. Course 2
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.

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

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

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

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

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

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

18. 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
Insert Lesson Title Here
–15
55
Course 2
Multiplying and Dividing Integers
30
–12˚F

19. 6. Lito wants to hand sanitizers for his family.
If there are 6 members in the family and
each sanitizer costs Php 55, how much does
he need to pay for the sanitizers.
7.During pandemic crisis , Ruth borrowed Php
12,000 from her sister to sustain their basic needs.
She promised to promised to pay for 6 months. How
much does she need to pay for each month?
8. Aileen invited her 3 friends for a visit to an
intimate birthday celebration. They rode a tricycle
that charged Php 18 per passenger. How much did
she pay for their fare expenses.

20. 9. There are 280 stranded
passengers because of lockdown. If a
bus can only accommodate 20
passengers, how many buses they
need?