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11-7 Multiplying Integers
Warm UpFind each product.
1. 8 • 4 2. 7 • 123. 3 • 9 4. 6 • 55. 80 • 6 6. 50 • 67. 40 • 90 8. 20 • 700
32 8427 30480 3003,600 14,000
11-7 Multiplying Integers
Learn to multiply integers.
11-7 Multiplying Integers
–66Product
–(2 + 2 + 2)2 + 2 + 2Addition
the opposite of 3 groups of 2
3 groups of 2Words
–3 • 23 • 2Numbers
11-7 Multiplying Integers
6–6Product
–[(–2) + (–2) + (–2)](–2) + (–2) + (–2)Addition
the opposite of 3 groups of –2
3 groups of –2Words
–3 • (–2)3 • (–2)Numbers
11-7 Multiplying Integers
Additional Example 1: Multiplying Integers
Find each product.
A. 5 • 2
B. 4 • (–5)
5 • 2 = 10 Think: 5 groups of 2.
4 • (–5) = –20 Think: 4 groups of –5.
To find the opposite of a number, change the sign. The opposite of 6 is –6. The opposite of –4 is 4.
Remember!
11-7 Multiplying Integers
Additional Example 1: Multiplying Integers
Find each product.
C. –3 • 2
D. –2 • (–4)
–3 • 2 = –6 Think: the opposite of 3 groups of 2.
–2 • (–4) = 8 Think: the opposite of 2 groups of –4.
11-7 Multiplying Integers
Check It Out: Example 1
Find each product.
A. 3 • 4
B. 2 • (–7)
3 • 4 = 12 Think: 3 groups of 4.
2 • (–7) = –14 Think: 2 groups of –7.
11-7 Multiplying Integers
Check It Out: Example 1
Find each product.
C. –5 • 3
D. –4 • (–6)
–5 • 3 = –15 Think: the opposite of 5 groups of 3.
–4 • (–6) = 24 Think: the opposite of 4 groups of –6.
11-7 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 • 9 = 0 (–12) • 0 = 0
11-7 Multiplying Integers
Additional Example 2: Evaluating Integer Expressions
Evaluate –7x for each value of x.
A. x = –3
B. x = 5
–7x Write the expression.–7 • (–3) Substitute –3 for x.21 The signs are the same, so the answer
is positive.
–7x Write the expression.
–7 • 5 Substitute 5 for x. –35 The signs are different,
so the answer is negative.
–7x means –7 • x.Remember!
11-7 Multiplying Integers
Check It Out: Example 2
Evaluate –4y for each value of y.
A. y = – 2
B. y = 7
–4y Write the expression.
–4 • (–2) Substitute –2 for y.
8 The signs are the same, so the answer is positive.
–4y Write the expression.
–4 • 7 Substitute 7 for y.
–28 The signs are different, so the answer is negative.
11-7 Multiplying Integers
Learn to divide integers.
11-7 Multiplying Integers
Multiplication and division are inverse operations. To solve a division problem, think of the related multiplication.
To find the mean of a list of numbers:
1. Add all the numbers together.
2. Divide by how many numbers are in the list.
Remember!
11-7 Multiplying Integers
Additional Example 1: Dividing Integers
Find each quotient.
A. –30 ÷ 6
B. –42 ÷ (–7)
Think: What number times 6 equals –30?
–5 • 6 = –30, so –30 ÷ 6 = –5.
Think: What number times –7 equals –42?
6 • (–7) = –42, so –42 ÷ (–7) = 6.
11-7 Multiplying Integers
Check It Out: Example 1
Find each quotient.
A. –15 ÷ 5
B. –36 ÷ (–6)
Think: What number times 5 equals –15?
–3 • 5 = –15, so –15 ÷ 5 = –3.
Think: What number times –6 equals –36?
6 • (–6) = –36, so –36 ÷ (–6) = 6.
11-7 Multiplying Integers
Dividing IntegersIf 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 = 0014__ 0
–11 __
You cannot divide any integer by 0.
Because division is the inverse of multiplication, the rules for dividing integers are the same as the rules for multiplying integers.
11-7 Multiplying Integers
Additional Example 2A: Evaluating Integer Expressions
Evaluate for each value of d.
d = 16
Write the expression.
= 16 ÷ 4 Substitute 16 for d.
= 4 The signs are the same, so the answer is positive.
d 4__
d 4__
16 4 __
11-7 Multiplying Integers
Additional Example 2B: Evaluating Integer Expressions
Evaluate for each value of d.
d = –24
Write the expression.
= –24 ÷ 4 Substitute –24 for d.
= –6 The signs are different, so the answer is negative.
d 4__
d 4__
-24 4 ___
11-7 Multiplying Integers
Additional Example 2C: Evaluating Integer Expressions
Evaluate for each value of d.
d = –12
Write the expression.
= –12 ÷ 4 Substitute –12 for d.
= –3 The signs are different, so the answer is negative.
d 4__
d 4__
-12 4 ___
