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Different signs; product is negative. Same signs; product is positive. Multiply 2 and – 5. Different signs; product is negative. Find the product. EXAMPLE 1 Multiply real numbers a. – 3 (6) b. 2 (–5) (–4) = 40 c. – (–4) (–3) 1 2 Multiply – and – 4 1 2 = – 6 = – 18 = 2 (– 3) (–10) (–4) =

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GUIDED PRACTICE for Example 1 Find the product. 1. – 2 (– 7)= 14 2. – 0.5 (– 4) (– 9)= – 18 3. (–3) (7) 4 3 = – 28

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Multiplicative property of – 1 Identity property of multiplication Commutative property of multiplication Associative property of multiplication Multiplicative property of zero Property illustratedStatement EXAMPLE 2 Identify properties of multiplication x (7 0.5) a. (x 7) 0.5 = b. 8 0 = 0 c. – 6 y = y (– 6) d. 9 (– 1) = – 9 e. 1 v = v

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GUIDED PRACTICE for Example 2 Identify the property illustrated. Multiplicative property of – 1 Commutative property of multiplication Associative property of multiplication Multiplicative property of zero Commutative property of multiplication Multiplicative property of – 1 4. –1 8 = – 8 12 x = x 125. y (4 9) (y 4) 9 = 6. 7. 0 (– 41) = 0 8. – 5 (– 6) = – 6 (– 5) 9. –13 (– 1) – 8 =

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Multiplicative property of – 1. Product of 0.25 and – 4 is – 1. Associative property of multiplication Commutative property of multiplication EXAMPLE 3 Identify properties of multiplication Find the product (–4x) 0.25. Justify your steps. = –x= –x 0.25 (–4x)(–4x) 0.25 = = (0.25 (–4))x = –1 x

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Lakes EXAMPLE 4 Solve a multi-step problem In 1900 the elevation of Mono Lake in California was about 6416 feet. From 1900 to 1950, the average rate of change in elevation was about – 0.12 foot per year.From 1950 to 2000, the average rate of change was about – 0.526 foot per year. Approximate the elevation in 2000.

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Substitute values. EXAMPLE 4 Solve a multi-step problem SOLUTION STEP 1 STEP 2 = 6416 + (–6) Multiply – 0.12 and 50. New elevation = Calculate the elevation in 1950. Use the elevation in 1900 as the original elevation. The time span 1950 – 1900 = 50 years. 6416 +(–0.12)(50) Write a verbal model. = 6410 Add 6416 and –6. New elevation (feet) Original elevation (feet) Average rate of change (feet/year) Time passed (years) = +

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New elevation = = 6383.7 Multiply – 0.526 and 50. Substitute values. EXAMPLE 4 Solve a multi-step problem STEP 3 = 6410 + (–26.3) Add 6410 and –26.3. Calculate the elevation in 2000. Use the elevation in 1950 as the original elevation. The time span 2000 – 1950 = 50 years. 6410 +(– 0.526)(50)

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EXAMPLE 4 Solve a multi-step problem ANSWER The elevation in 2000 was about 6383.7 feet above sea level.

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GUIDED PRACTICE for Example 3 and 4 Find the product. Justify your steps. 3 10 10. (5y) = ( 5)y 3 10 Associative property of multiplication 3 2 = y Product of and 5 is. 3 10 3 2 3 2 = y Multiplicative property of. 3 2

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GUIDED PRACTICE for Example 3 and 4 0.8 (–x) (–1) 11. 0.8 (–1) (–x) = Multiplicative property of –1 Commutative property of multiplication = 0.8x Multiply = – 0.8 (–x)

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GUIDED PRACTICE for Example 3 and 4 Product of – 0.5 and – 6 is 3. = –3y Commutative property of multiplication 12. (–y)(–0.5)(–6) = (–y)(3)

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GUIDED PRACTICE for Example 3 and 4 Using the data in Example 4, approximate the elevation of Mono Lake in 1925 and in 1965. 13. ANSWER about 6413 ft; about 6402.11 ft

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EXAMPLE 1 Factor when b is negative and c is positive

EXAMPLE 1 Factor when b is negative and c is positive

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