EXAMPLE 1

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EXAMPLE 1. Multiplying Integers. Diving A diver is swimming downward to explore a coral reef. The diver’s depth is changing by –2 feet per second. The diver started at sea level. What is the diver’s position relative to sea level after 10 seconds? after 30 seconds?. SOLUTION.

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EXAMPLE 1

Multiplying Integers

Diving A diver is swimming downward to explore a coral reef. The diver’s depth is changing by –2 feet per second. The diver started at sea level. What is the diver’s position relative to sea level after 10 seconds? after 30 seconds?

SOLUTION

a. To find the diver’s position relative to sea level after 10 seconds, use the distance formula d = rt.

d= rt

Write the distance formula.

d = –2 (10)

Substitute –2 for r and 10 for t.

d = –20

Different signs, so product is negative.

The diver’s position relative to sea level is –20 feet.

b. Find the diver’s position relative to sea level after

30 seconds.

(30)

d

–2

=

d

= – 60

The diver’s position relative to sea level is –60 feet.

EXAMPLE 1

Multiplying Integers

d= rt

Write the distance formula.

Substitute –2 for r and 30 for t.

Different signs, so product is negative.

EXAMPLE 2

Multiplying Two or More Integers

a. –1(6)

= –6

Different signs, so product is negative.

b. –8(–2)

= 16

Same sign, so product is positive.

c. –15(0)

= 0

Product of an integer and 0 is 0.

d. 4(–10)(–12)

= –40(–12)

Multiply from left to right.

= 480

Multiply.

a2

+ 3b whena = –5 andb = –11.

Evaluate

a2

+ 3b

= (–5)2

+ 3(–11)

EXAMPLE 3

Evaluating an Expression with Integers

SOLUTION

Substitute –5 fora and –11 for b.

= 25 + 3(–11)

Evaluate the power.

= 25 + (–33)

Multiply.

= –8

d = –2

(13)

The diver’s position relative to sea level is –26 feet.

GUIDED PRACTICE

for Examples 1, 2 and 3

1. What If? In Example 1, what is the diver’s position relative to sea level after 13 seconds?

SOLUTION

To find the diver’s position relative to sea level after 13 seconds, use the distance formula d = rt.

d = rt

Write the distance formula.

Substitute –2 for r and 13 for t.

d = –26

Different signs, so product is negative.

GUIDED PRACTICE

for Examples 1, 2 and 3

Find the product.

2. –1(4)

= –4

Different signs, so product is negative.

3. 7(0)

= 0

Product of an integer and 0 is 0.

4. –6(–11)

= 66

Same sign, so product is positive.

5. –1(–12)(–9)

= 12(–9)

Multiply from left to right.

= –108

Multiply.

GUIDED PRACTICE

for Examples 1, 2 and 3

Evaluate the expression when a = 3, b = –4, and c = –8 .

6. ac – b

= 3(–8) – (–4)

Substitute 3 for a , –4 for b and –8 for c.

= (–24) – (–4)

Multiply.

= –20

Subtract.

Substitute 3 for a , –4 for b and –8 for c.

7. ac + b

= 3(–8) + (–4)

= (–24) + (–4)

Multiply.

= –28

+ bc

8 a2

+ (–4) (–8)

= (3)2

GUIDED PRACTICE

for Examples 1, 2 and 3

Evaluate the expression when a = 3, b = –4, and c = –8 .

.

Substitute 3 for a , –4 for b and –8 for c.

= 9 + (–4)(–8)

Evaluate the power.

= 9 + 32

Multiply.

= 41

9 ab

–c2

= 3(–4) –

(–8)2

GUIDED PRACTICE

for Examples 1, 2 and 3

Evaluate the expression when a = 3, b = –4, and c = –8 .

.

Substitute 3 for a , –4 for b and –8 for c.

= 3(–4) – 64

Evaluate the power.

= (–12) – 64

Multiply.

= –76

Subtract.