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Multiplicative property of – 1 .

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

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Multiplicative property of – 1 .

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

  2. 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.

  3. New elevation (feet) Original elevation (feet) Time passed (years) Average rate of change (feet/year) + • = EXAMPLE 4 Solve a multi-step problem 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.

  4. 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 = 50years. 6410 +(– 0.526)(50) New elevation = Substitute values. = 6410 + (–26.3) Multiply –0.526 and 50. =6383.7 Add 6410 and –26.3.

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

  6. 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 = = for Example 3 and 4 GUIDED PRACTICE Find the product. Justify your steps. Associative property of multiplication

  7. 11. 0.8 (–1)(–x) 0.8 (–x)(–1) = for Example 3 and 4 GUIDED PRACTICE Commutative property of multiplication Multiplicative property of –1 = – 0.8 (–x) = 0.8x Multiply

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

  9. 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 for Example 3 and 4 GUIDED PRACTICE

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