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Integers Multiplying and Dividing

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EXAMPLE 1 Multiplying Integers a. –5 ( –7 ) The product of two integers with the same sign is positive. b. –8 ( 2 ) The product of two integers with different signs is negative. c. –12 ( 0 ) The product of an integer and 0 is 0. = 35 = –16 = 0

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EXAMPLE 2 Evaluating Variable Expressions a. Evaluate a 2 when a = –3. b. Evaluate xyz when x = 2, y = –4, and z = 6. SOLUTION Substitute – 3 for a. = –3 ( –3 ) Write – 3 as a factor two times. = 9 Multiply – 3 and – 3. Substitute 2 for x, – 4 for y, and 6 for z. = –8 ( 6 ) = –48 Multiply 2 and – 4. Multiply – 8 and 6. a. a 2 b. xyz = (–3) 2 = 2(–4)(6)

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EXAMPLE 3 Using Integer Multiplication Greenland Most of Greenland is covered with ice that is almost two miles thick in some places. Scientists estimate that 3 feet of this ice melts each year. Find the change in the thickness of the ice after 10 years.

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EXAMPLE 3 ANSWER The thickness of the ice will decrease 30 feet in 10 years. Change in ice thickness = –3 ( 10 ) = –30 SOLUTION You can find the total change in the ice thickness by multiplying the yearly change by the number of years. Use – 3 for the yearly change because the thickness of the ice decreases by 3 feet each year. Using Integer Multiplication

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GUIDED PRACTICE Find the product. 1. –9(2) 2. –3(–4) ANSWER –18 ANSWER 12 3. 5(–5) ANSWER –25 4. 0(–14) ANSWER 0

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GUIDED PRACTICE 5. Evaluate the expressions x 2 y and –3xy 2 when x = –2 and y = 3. ANSWER 12, 54 ANSWER – 54 ft What If? What is the change in the thickness of the ice in Example 3 after 18 years? 6.

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Dividing Integers EXAMPLE 1 The quotient of two integers with different signs is negative. The quotient of two integers with the same sign is positive. The quotient of 0 and any nonzero integer is 0. a. 28 (–4) = –7 –60 –12 b.b. = 5 = 0 c. 0 (–13)

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GUIDED PRACTICE Find the quotient. ANSWER 0 1. 24 6 – ANSWER 4 – 2. 0 2 – 3. 39 13 – – 4.19 ( 1 ) – 3 ANSWER 19 – ANSWER

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Rule for Multiply and Dividing Integers Multiplication: Same Signs: Multiply the absolute values, positive product Different Signs: Multiply the absolute values; negative product Division: Same Signs: Divide absolute values, positive quotient Different Signs: Divide absolute values, negative quotient.

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