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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? 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. SOLUTION

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EXAMPLE 1 Multiplying Integers d = rt Write the distance formula. Substitute –2 for r and 30 for t. Different signs, so product is negative. The diver’s position relative to sea level is –20 feet. ANSWER The diver’s position relative to sea level is –60 feet. b. Find the diver’s position relative to sea level after 30 seconds. d (30) –2 = d = – 60

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EXAMPLE 2 a. –1(6) b. –8(–2) c. –15(0) d. 4(–10)(–12) = 480 Different signs, so product is negative. Same sign, so product is positive. Product of an integer and 0 is 0. Multiply from left to right. Multiply. Multiplying Two or More Integers = –6 = 16 = 0 = –40(–12)

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EXAMPLE 3 Evaluating an Expression with Integers Evaluate a2a2 + 3b when a = –5 and b = – b a2a2 SOLUTION + 3(–11) = (–5) 2 = (–11) Substitute –5 for a and –11 for b. Evaluate the power. = 25 + (–33) = –8 Multiply. Add.

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GUIDED PRACTICE for Examples 1, 2 and 3 d = rt Write the distance formula. Substitute –2 for r and 13 for t. d = –26 Different signs, so product is negative. To find the diver’s position relative to sea level after 13 seconds, use the distance formula d = rt. SOLUTION d = –2 (13) 1. What If? In Example 1, what is the diver’s position relative to sea level after 13 seconds? The diver’s position relative to sea level is –26 feet. ANSWER

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GUIDED PRACTICE for Examples 1, 2 and 3 2. –1(4) 4. –6(–11) 5. –1(–12)(–9) = –108 Different signs, so product is negative. Same sign, so product is positive. Product of an integer and 0 is 0. Multiply from left to right. Multiply. Find the product. = –4 3. 7(0) = 0 = 66 = 12(–9)

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GUIDED PRACTICE for Examples 1, 2 and 3 Evaluate the expression when a = 3, b = –4, and c = –8. 6. ac – b Substitute 3 for a, –4 for b and –8 for c. = 3(–8) – (–4) = (–24) – (–4) = –20 Subtract. Multiply. 7. ac + b Substitute 3 for a, –4 for b and –8 for c. = 3(–8) + (–4) = (–24) + (–4) Multiply. = –28 Add.

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GUIDED PRACTICE for Examples 1, 2 and 3 + bc 8 a 2 + (–4) (–8) = (3) 2 Evaluate the power. = = 41 Multiply. Add. Substitute 3 for a, –4 for b and –8 for c. = 9 + (–4)(–8). Evaluate the expression when a = 3, b = –4, and c = –8.

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GUIDED PRACTICE for Examples 1, 2 and 3 9 ab– c2– c2 = 3(–4) – (–8) 2 Evaluate the power. = –76 Multiply. Subtract. Substitute 3 for a, –4 for b and –8 for c. = 3(–4) – 64 = (–12) – 64. Evaluate the expression when a = 3, b = –4, and c = –8.

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