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Warm Up

Multiply Real Numbers. Warm Up. Lesson Presentation. Lesson Quiz. Associative property of addition. –11.1. ANSWER. ANSWER. Identity property of addition. 32.7. ANSWER. ANSWER. ?. ?. Warm-Up. 1. –17.3 + 6.2 =. 2. 26.9 – (–5.8) =. Identify the property illustrated.

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Warm Up

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  1. Multiply Real Numbers Warm Up Lesson Presentation Lesson Quiz

  2. Associative property of addition –11.1 ANSWER ANSWER Identity property of addition 32.7 ANSWER ANSWER ? ? Warm-Up 1. –17.3 + 6.2 = 2. 26.9 – (–5.8) = Identify the property illustrated. 3. (12 + 14) + 82 = 12 + (14 + 82) 4. –3 + 0 = –3

  3. $10 million ANSWER Warm-Up 5.A company had a profit of –$8.6 million in 2005 and $1.4 million in 2006. What is the change in profit?

  4. (–10) (–4) = 1 2 1 c. – (–4) (–3) Multiply – and –4 2 Example 1 Find the product. a. – 3 (6) Different signs; product is negative. = – 18 b. 2 (–5) (–4) Multiply2and –5. Same signs; product is positive. = 40 = 2 (– 3) = – 6 Different signs; product is negative.

  5. 4 3 3. (–3) (7) Guided Practice Find the product. 1. – 2 (– 7) = 14 2. – 0.5 (– 4) (– 9) = – 18 = – 28

  6. a.(x 7) 0.5 = x (7 0.5) b.8 0 = 0 y (– 6) c.– 6 y = d.9 (– 1) = – 9 Example 2 Identify the property illustrated. Statement Property illustrated Associative property of multiplication Multiplicative property of zero Commutative property ofmultiplication Multiplicative property of – 1

  7. 4. –1 8 = – 8 5. x 12 12 x = (y 4) 9 = y (4 9) 6. 7. 0 (– 41) = 0 – 6 – 5 (– 6) = 8. (– 5) –13 (– 1) – 8 9. = Guided Practice Identify the property illustrated. Multiplicative property of – 1 Commutative property ofmultiplication Associative property of multiplication Multiplicative property of zero Commutative property ofmultiplication Multiplicative property of – 1

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

  9. 11. 0.8 (–1)(–x) 0.8 (–x)(–1) = 3 3 (5y) 10. ( 5)y = 10 10 3 3 3 Product of and 5 is . 10 2 2 y Multiplicative property of . y 3 3 2 2 = = Guided Practice Find the product. Justify your steps. Associative property of multiplication Commutative property of multiplication Multiplicative property of –1 = – 0.8 (–x) = 0.8x Multiply

  10. (–y)(–0.5)(–6) 12. Guided Practice Find the product. Justify your steps. Product of –0.5 and –6 is 3. = (–y)(3) = –3y Commutative property of multiplication

  11. Example 4 Lakes 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.

  12. Example 4 SOLUTION STEP 1 Write a verbal model. STEP 2 Calculate the elevation in 1950. Use the elevation in 1900 as the original elevation. The time span 1950 – 1900 = 50years. New elevation = 6416 +(–0.12)(50) Substitute values. = 6416 + (–6) Multiply –0.12 and 50. =6410 Add 6416 and –6.

  13. ANSWER The elevation in 2000 was about 6383.7 feet above sea level. Example 4 STEP 3 Calculate the elevation in 2000. Use the elevation in 1950 as the original elevation. The time span 2000 – 1950 = 50years. 6410 +(– 0.526)(50) New elevation = Substitute values. = 6410 + (–26.3) Multiply –0.526 and 50. =6383.7 Add 6410 and –26.3.

  14. ANSWER 13. Using the data in Example 4, approximate the elevation of Mono Lake in 1925 and in 1965. about 6413 ft; about 6402.11 ft Guided Practice

  15. ANSWER 52 –26.64 ANSWER 4.–y (–1) = y 3.r 0 = 0 Multiplicative property of –1 Multiplicative property of zero ANSWER ANSWER Lesson Quiz Find the product. 1.–6.5(4)(–2) 2.7.4(– 1.2)(3) Identify the property illustrated.

  16. Since Javier began setting his thermostat lower, his energy bills have been declining at a rate of – 0.88 dollar per year. If his average bill was $130 in 1990, estimate his average bill in 2005. 5. $116.80 ANSWER Lesson Quiz

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