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Applying the Distributive Property - Warm-Up Lesson Presentation, Lesson, Quiz

This is a comprehensive lesson on applying the distributive property. It includes warm-up exercises, a lesson presentation, and a quiz.

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Applying the Distributive Property - Warm-Up Lesson Presentation, Lesson, Quiz

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  1. Apply the Distributive Property Warm Up Lesson Presentation Lesson Quiz

  2. –18 –72b ANSWER ANSWER 24x ANSWER ? ? ? Warm-Up 1. –15 + (–19) + 16 = 2. 6(–x)(–4) = 3. –9(–2)(–4b) =

  3. $96.80 ANSWER Warm-Up 4.Kristin paid $1.90 per black-and-white photo b and $6.80 per color photo c to have some photos restored. What was the total amount A that she paid if she had 8 black-and-white and 12 color photos restored?

  4. Example 1 Use the distributive property to write an equivalent expression. a.4(y + 3) = 4y + 12 b.(y + 7)y = y2 + 7y c.n(n – 9) = n2 – 9n 16 – 8n d. (2 – n)8 =

  5. Multiplicative property of –1 Example 2 Use the distributive property to write an equivalent expression. a.–2(x + 7)= – 2(x) + – 2(7) Distribute –2. =– 2x – 14 Simplify. b. (5 – y)(–3y) = 5(–3y) – y(–3y) Distribute – 3y. =– 15y + 3y2 Simplify. c.–(2x – 11) = (–1)(2x – 11) = (– 1)(2x)– (–1)(11) Distribute – 1. = – 2x + 11 Simplify.

  6. 1 2 4. (2n + 6) Guided Practice Use the distributive property to write an equivalent expression. 1.2(x + 3) = 2x + 6 2.– (4– y)= – 4+ y 3.(m – 5)(– 3m) = – 3m2 + 15m = n + 3

  7. Example 3 Identify the terms, like terms, coefficients, and constant terms of the expression 3x – 4 – 6x + 2. SOLUTION Write the expression as a sum: 3x + (–4) + (–6x) + 2 Terms: 3x, – 4, – 6x, 2 Like terms: 3xand – 6x; – 4 and 2 Coefficients: 3, – 6 Constant terms: – 4, 2

  8. ANSWER Terms: –7y, 8, – 6y, – 13 Guided Practice Identify the terms, like terms, coefficients, and constant terms of the expression –7y + 8 – 6y – 13. Like terms: –7yand – 6y , 8 and –13; Coefficients: –7, – 6 Constant terms: 8, – 13

  9. n +3 n + 30 5n + 3 5n + 30 C A B D ANSWER The correct answer is B. A B C D Example 4 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.

  10. Guided Practice 6. Simplify the expression5(6+ n) – 2(n – 2) =34 + 3n.

  11. Example 5 EXERCISING 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 rbe 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. SOLUTION The workout lasts 50 minutes, and your running time is rminutes. So, your swimming time is (50 – r) minutes.

  12. C= 5 r +9(50– r) Example 5 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.

  13. ANSWER You burn 570 calories in your 50 minute workout if you run for 20 minutes. Example 5 STEP2 Find the value of Cwhen r= 20. C = 6r+ 450 Write equation. = 6(20)+450 = 570 Substitute 20 for r. Then simplify.

  14. 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 7. WHAT IF? In Example 5, suppose your workout lasts 45 minutes. How many calories do you burn if you run for 20 minutes?30 minutes?

  15. – 4. (3x 2)4 x + – – 1. 6(2 x) ANSWER 13x 8 – – ANSWER 12 6x 3x 2 2.x(3x 2) – + – ANSWER 3x2 – 2x 3. 4x 5 3 x – – + ANSWER Lesson Quiz Use the distributive property to write an equivalent expression. Simplify the expression.

  16. You burn 18 calories per minute on an elliptical trainer and 7 calories per minute weight training. Suppose you work out at these two activities for 45 minutes. How many calories do you burn if you lift weights for 30 minutes? 5. ANSWER 480 calories Lesson Quiz

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