1. 2.4 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Multiply Real Numbers

2. 2.4 Warm-Up 1.–17.3 + 6.2 = ANSWER –11.1 2.26.9 – (–5.8) = ANSWER 32.7 ? ? 3.(12 + 14) + 82 = 12 + (14 + 82) ANSWER Associative property of addition 4.–3 + 0 = –3 ANSWER Identity property of addition Identify the property illustrated.

3. 2.4 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? ANSWER $10 million

4. 2.4 Example 1 Different signs; product is negative. Same signs; product is positive. Multiply 2 and – 5. Different signs; product is negative. Find the product. a. – 3 (6) b. 2 (–5) (–4) = 40 c. – (–4) (–3) 1 2 Multiply – and – 4 1 2 = – 6 = – 18 = 2 (– 3) (–10) (–4) =

5. 2.4 Guided Practice Find the product. 1. – 2 (– 7)= 14 2. – 0.5 (– 4) (– 9)= – 18 3. (–3) (7) 4 3 = – 28

6. 2.4 Example 2 Multiplicative property of – 1 Commutative property of multiplication Associative property of multiplication Multiplicative property of zero Property illustratedStatement x (7 0.5) a. (x 7) 0.5 = b. 8 0 = 0 c. – 6 y = y (– 6) d. 9 (– 1) = – 9 Identify the property illustrated.

7. 2.4 Guided Practice 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 =

8. 2.4 Example 3 Multiplicative property of – 1. Product of 0.25 and – 4 is – 1. Associative property of multiplication Commutative property 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

9. 2.4 Guided Practice 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 0.8 (–x) (–1) 11. 0.8 (–1) (–x) = Multiplicative property of –1 Commutative property of multiplication = 0.8x Multiply = – 0.8 (–x)

10. 2.4 Guided Practice Product of – 0.5 and – 6 is 3. = –3y Commutative property of multiplication 12. (–y)(–0.5)(–6) = (–y)(3) Find the product. Justify your steps.

11. 2.4 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. 2.4 Example 4 Substitute values. 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.

13. 2.4 Example 4 New elevation = = 6383.7 Multiply – 0.526 and 50. Substitute values. 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) ANSWER The elevation in 2000 was about 6383.7 feet above sea level.

14. 2.4 Guided Practice 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

15. 2.4 Lesson Quiz Find the product. 1. –6.5(4)(–2) ANSWER 52 2. 7.4(– 1.2)(3) ANSWER –26.64 4. –y (–1) = y ANSWER Multiplicative property of –1 Identify the property illustrated. ANSWER Multiplicative property of zero 3. r 0 = 0

16. 2.4 Lesson Quiz ANSWER $116.80 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.