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11-6 Multiplying & Dividing Integers
Warm Up
Problem of the Day
Lesson Presentation
Course 1
11-6 Multiplying Integers
Warm Up
Find each product.
1.
3.
5.
7.
Course 1
8•4
3•9
80 • 6
40 • 90
32
27
480
3,600
2.
4.
6.
8.
7 • 12
84
6•5
30
50 • 6
300
20 • 700 14,000
Notes on Multiplying and Dividing
Integers
• Steps
– Multiply and Divide as usual.
– When there is an even amount of negative
signs, the final answer is positive.
– When there is an odd amount of negative
signs, the final answer is negative.
Examples
 3  4  12
 3  4  12
 3  4  2  24
 3  4  2  1  24
 24  2  12
 24  2  1  12
11-6 Multiplying Integers
Numbers
3•2
–3 • 2
Words
3 groups of 2
the opposite of 3
groups of 2
Addition
2+2+2
–(2 + 2 + 2)
Product
6
–6
Course 1
11-6 Multiplying Integers
Numbers
Words
Addition
Product
Course 1
3 • (–2)
–3 • (–2)
3 groups of –2
the opposite of 3
groups of –2
(–2) + (–2) + (–2) –[(–2) + (–2) + (–2)]
–6
6
11-7 Dividing Integers
Because division is the inverse of multiplication,
the rules for dividing integers are the same as the
rules for multiplying integers.
Dividing Integers
If the signs are the same, the product is positive.
24 ÷ 3 = 8
–6 ÷ (–3) = 2
If the signs are different, the quotient is negative.
–20 ÷ 5 = –4
72 ÷ (–8) = –9
Zero divided by any integer equals 0.
0
0
__
__
=0
=0
–11
14
You cannot divide any integer by 0.
Course 1
11-6 Multiplying Integers
Additional Example 1: Multiplying Integers
Find each product.
A. 5 • 2
5 • 2 = 10
Think: 5 groups of 2.
B. 4 • (–5)
4 • (–5) = –20
Think: 4 groups of –5.
Remember!
To find the opposite of a number, change the sign.
The opposite of 6 is –6. The opposite of –4 is 4.
Course 1
11-6 Multiplying Integers
Additional Example 1: Multiplying Integers
Find each product.
C. –3
•
2
–3
•
2 = –6
D. –2
•
(–4)
–2
•
(–4) = 8 Think: the opposite of 2 groups of –4.
Course 1
Think: the opposite of 3 groups of 2.
11-6 Multiplying Integers
Check It Out: Example 1
Find each product.
A. 3 • 4
3 • 4 = 12
Think: 3 groups of 4.
B. 2 • (–7)
2 • (–7) = –14
Course 1
Think: 2 groups of –7.
11-6 Multiplying Integers
Check It Out: Example 1
Find each product.
C. –5
•
3
–5
•
3 = –15 Think: the opposite of 5 groups of 3.
D. –4
•
(–6)
–4
•
(–6) = 24 Think: the opposite of 4 groups of –6.
Course 1
11-6 Multiplying Integers
MULTIPLYING INTEGERS
If the signs are the same, the product is positive.
4 • 3 = 12
–6 • (–3) = 18
If the signs are different, the product is negative.
–2 • 5 = –10
7 • (–8) = –56
The product of any number and 0 is 0.
0
Course 1
•
9=0
(–12)
•
0=0
11-7 Dividing Integers
Additional Example 1: Dividing Integers
Find each quotient.
A. –30 ÷ 6
Think: What number times 6 equals –30?
–5
•
6 = –30, so –30 ÷ 6 = –5.
B. –42 ÷ (–7)
Think: What number times –7 equals –42?
6
Course 1
•
(–7) = –42, so –42 ÷ (–7) = 6.
11-6 Multiplying Integers
Additional Example 2: Evaluating Integer
Expressions
Evaluate –7x for each value of x.
A. x = –3
–7x
Write the expression.
–7 • (–3) Substitute –3 for x.
The signs are the same, so the answer
21
is positive.
B. x = 5
–7x Write the expression.
–7 • 5 Substitute 5 for x.
–35 The signs are different,
so the answer is
negative.
Course 1
Remember!
–7x means –7
•
x.
11-6 Multiplying Integers
Check It Out: Example 2
Evaluate –4y for each value of y.
A. y = – 2
–4y
Write the expression.
–4 • (–2) Substitute –2 for y.
8
The signs are the same, so the answer
is positive.
B. y = 7
–4y
Write the expression.
–4 • 7
–28
Course 1
Substitute 7 for y.
The signs are different, so the answer
is negative.
11-6 Multiplying
Insert Lesson
Integers
Title Here
Lesson Quiz
Find each product.
1. 6
•
3. –9
(4) 24
•
(–2) 18
2. 3
•
4. –6
(–2) –6
•
5 –30
5. Evaluate 3y for y = –7. –21
6. During a football game, Raymond’s team lost 6
yards on each of 3 plays and gained 8 yards
on each of two plays. What integer represents
the total change in the team’s position?
–2
Course 1