Lesson 2 4 Multiply Real Numbers You will

Lesson 2. 4 Multiply Real Numbers You will multiply real numbers

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

for Example 1 GUIDED PRACTICE Find the product. 1. – 2 (– 7) = (– 2) (– 7) = 14 2. – 0. 5 (– 4) (– 9) 3. 4 (– 3) (7) 3 Same signs; product is positive. = (2) (– 9) Multiply – 0. 5 and – 4. = – 18 Different signs; product is negative. Multiply 4 and – 3. 3 = – 4 (7) = – 28 Different signs; product is negative.

EXAMPLE 2 Identify properties of multiplication Statement Property illustrated a. (x b. 8 0 =0 c. – 6 y = y (– 6) d. 9 (– 1) = – 9 e. 1 v= v 7) 0. 5 = x (7 0. 5) Associative property of multiplication Multiplicative property of zero Commutative property of multiplication Multiplicative property of – 1 Identity property of multiplication

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

EXAMPLE 3 Identify properties of multiplication Find the product (– 4 x) 0. 25 = 0. 25. Justify your steps. (– 4 x) = (0. 25 (– 4))x Commutative property of multiplication Associative property of multiplication =– 1 x Product of 0. 25 and – 4 is – 1. =–x Multiplicative property of – 1.

EXAMPLE 4 Solve a multi-step problem 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.

EXAMPLE 4 Solve a multi-step problem SOLUTION STEP 1 Write a verbal model. New elevation (feet) = Original elevation (feet) + Average rate of change (feet) • Time passed (feet) STEP 2 Calculate the elevation in 1950. Use the elevation in 1900 as the original elevation. The time span 1950 – 1900 = 50 years. New elevation = 6416 +(– 0. 12)(50) Substitute values. = 6416 + (– 6) Multiply – 0. 12 and 50. = 6410 Add 6416 and – 6.

EXAMPLE 4 Solve a multi-step problem STEP 3 Calculate the elevation in 2000. Use the elevation in 1950 as the original elevation. The time span 2000 – 1950 = 50 years. New elevation = 6410 +(– 0. 526)(50) Substitute values. = 6410 + (– 26. 3) Multiply – 0. 526 and 50. = 6383. 7 Add 6410 and – 26. 3

EXAMPLE 4 Solve a multi-step problem ANSWER The elevation in 2000 was about 6383. 7 feet above sea level.

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

GUIDED PRACTICE 11. for Example 3 and 4 0. 8 (– x) (– 1) = 0. 8 (– 1) (–x) Commutative property of multiplication = (0. 8) (– 1)) –x Associative property of multiplication = – 0. 8 –x Product of 0. 8 and – 1 is – 0. 8. Multiplicative property of 0. 8. = 0. 8 x

GUIDED PRACTICE for Example 3 and 4 12. (– y)(– 0. 5)(– 6) = (– 0. 5)(– 6 ) (–y) Commutative property of multiplication = ((– 0. 5) (– 6)) – y Associative property of multiplication = 3 = – 3 y –y Product of – 0. 5 and – 6 is 3. Multiplicative property of 3.

GUIDED PRACTICE 12. for Example 3 and 4 Using the data in Example 4, approximate the elevation of Mono Lake in 1925 and in 1965. SOLUTION STEP 1 Write a verbal model. New elevation (feet) = Original elevation (feet) + Average rate of change (feet) • Time passed (feet) STEP 2 Calculate the elevation in 1950. Use the elevation in 1900 as the original elevation. The time span 1950 – 1900 = 50 years.

GUIDED PRACTICE for Example 3 and 4 New elevation = 6416 + (– 0. 12)(50) Substitute values. = 6416 + (– 6) Multiply – 0. 12 and 50. = 6410 Add 6416 and – 6. STEP 3 Calculate the elevation in 1925. Use the elevation in 1900 as the original elevation. The time span 1925 – 1900 = 25 years.

GUIDED PRACTICE for Example 3 and 4 New elevation = 6416 +(– 0. 12)(25) Substitute values. = 6416 + (– 3) Multiply – 0. 12 and 25. = 6413 Add 6416 and – 3.

GUIDED PRACTICE for Example 3 and 4 STEP 4 Calculate the elevation in 1965. Use the elevation in 1950 as the original elevation. The time span 1965 – 1950 = 15 years. New elevation = 6410 +(– 0. 526)(15) Substitute values. = 6410 + (– 7. 89) Multiply – 0. 526 and 15. = 6402. 11 Add 6410 and – 7. 89.