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Algebra 1

Algebra 1. 2.5 Distributive Property. Equivalent expressions : two expressions that have the same output value for every input value Distributive Property : multiply the outside number to every number in the parenthesis Term : the individual parts of an expression. Vocabulary.

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Algebra 1

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  1. Algebra 1 2.5 Distributive Property

  2. Equivalent expressions: two expressions that have the same output value for every input value • Distributive Property: multiply the outside number to every number in the parenthesis • Term: the individual parts of an expression Vocabulary

  3. Coefficient: the number part of a term • Constant Term: a term that has a number part but no variable • Like Terms: terms that have the same variable part Vocabulary

  4. EXAMPLE 1 Apply the distributive property Use the distributive property to write an equivalent expression. 1.4(y + 3) = 4y + 12 2.(y + 7)y = y2 + 7y 3.n(n – 9) = n2 – 9n 4. (2 – n)8 = 16 –8n

  5. EXAMPLE 2 Distribute a negative number Use the distributive property to write an equivalent expression. 1.–2(x + 7)= – 2(x) + – 2(7) Distribute –2. =– 2x – 14 Simplify. 2. (5 – y)(–3y) = 5(–3y) – y(–3y) Distribute – 3y. =– 15y + 3y2 Simplify.

  6. Multiplicative property of 21 EXAMPLE 2 Distribute a negative number (–1)(2x – 11) 3.–(2x – 11) = = (– 1)(2x)– (–1)(11) Distribute – 1. =–2x +11 Simplify.

  7. EXAMPLE 3 Identify parts of an expression Identify the terms, like terms, coefficients, and constant terms of the expression 3x – 4 – 6x + 2. SOLUTION Coefficients: 3, – 6 Terms: 3x, – 4, – 6x, 2 Constant terms: – 4, 2 Like terms: 3xand – 6x; – 4 and 2

  8. 1 1 1 1 2 2 2 2 2n + 6 4. (2n + 6) = Distribute GUIDED PRACTICE Use the distributive property to write an equivalent expression. 1.2(x + 3) = 2x + 6 2.– (4– y)= – 4+ y Distributive – 1 m (– 3m) –5 (– 3m) 3.(m – 5)(– 3m)= Distributive – 3m = – 3m2 + 15m Simplify. = n + 3 Simplify.

  9. GUIDED PRACTICE Identify the terms, like terms, coefficients, and constant terms of the expression –7y + 8 – 6y – 13. SOLUTION Terms: –7y, 8, – 6y, – 13 Like terms: –7yand – 6y , 8 and –13; Coefficients: –7, – 6 Constant terms: 8, – 13

  10. n +3 n + 30 5n + 3 5n + 30 C A B D ANSWER The correct answer is B. A B C D EXAMPLE 4 Standardized Test Practice Simplify the expression4(n+ 9)– 3(2 + n). 4(n + 9) – 3(2 + n) = 4n + 36 – 6 – 3n Distributive property =n +30 Combine like terms.

  11. GUIDED PRACTICE 1. Simplify the expression5(6+ n)– 2(n– 2). SOLUTION 5(6+ n) – 2(n– 2) = 30+ 5n – 2n + 4 Distributive property =3n + 34 Combine like terms.

  12. Your daily workout plan involves a total of 50 minutes of running and swimming. You burn 15 calories per minute when running and 9 calories per minute when swimming. Let r be the number of minutes that you run. Find the number of calories you burn in your 50 minute workout if you run for 20 minutes. EXAMPLE 5 Solve a multi-step problem SOLUTION The workout lasts 50 minutes, and your running time is rminutes. So, your swimming time is (50 – r) minutes.

  13. Amount burned (calories) Swimming time(minutes) Running time (minutes) Burning rate when swimming (calories/minute) Burning rate when running (calories/minute) = + • • C= 15 r + 9(50– r) EXAMPLE 5 Solve a multi-step problem STEP1 Write a verbal model. Then write an equation. C = Write equation. 15r + 9(50 – r) =15r + 450–9r Distributive property = 6r + 450 Combine like terms.

  14. ANSWER You burn 570 calories in your 50 minute workout if you run for 20 minutes. EXAMPLE 5 Solve a multi-step problem STEP2 Find the value of Cwhen r = 20. C = 6r+ 450 Write equation. = 6(20)+450 = 570 Substitute 20 for r. Then simplify.

  15. GUIDED PRACTICE WHAT IF… Suppose your workout lasts 45 minutes. How many calories do you run for 20 minutes? 30 minutes? SOLUTION The workout lasts 45 minutes, and your running time is rminutes. So, your swimming time is (45 – r) minutes.

  16. Amount burned (calories) Swimming time(minutes) Running time (minutes) Burning rate when swimming (calories/minute) Burning rate when running (calories/minute) = + • • C= 15 r + 9(45– r) 15 r + 9 (45 – r) GUIDED PRACTICE STEP1 Write a verbal model. Then write an equation. C = Write equation. =15r + 405–9r Distributive property = 6r + 405 Combine like terms.

  17. GUIDED PRACTICE STEP2 Find the value of Cwhen r = 20. C = 6r+ 405 Write equation. = 6(20)+405 = 525 Substitute 20 for r. Then simplify. STEP3 Find the value of Cwhen r = 30. 6r+ 405 C = Write equation. = 6(30)+405 = 585 Substitute 30 for r. Then simplify.

  18. ANSWER You burn 525 calories in your 45 minute workout if you run for 20 minutes. You burn 585 calories in your 45 minute workout if you run for 30 minutes. GUIDED PRACTICE

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