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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. Warm Up. Determine whether the ratios are proportional. Evaluate the expression. (16 – 8)  3 + (100  10). 5 8. 15 24. ,. 1. yes. 16 25. 12 15. ,. 2. no. A. 2 B. 18 C. 34 D. 104. 15 10. 20 16. ,.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up Determine whether the ratios are proportional. Evaluate the expression. (16 – 8)  3 + (100  10) 5 8 15 24 , 1. yes 16 25 12 15 , 2. no A. 2 B. 18 C. 34 D. 104 15 10 20 16 , 3. no 14 18 42 54 , yes 4.

  3. California Standards Number Sense (NS1.3) - Use proportions to solve problems (e.g., determine the value of N if = , find the length of a side of a polygon similar to a known polygon).Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Also covered: AF2.2, AF2.3 N 21 4 7

  4. Objective: You will learn how to solve proportions by using cross products.

  5. Vocabulary cross product

  6. For two ratios, the product of the numerator in one ratio and the denominator in the other is a cross product. If the two ratios form a proportion, then the cross products are equal. 5 · 6 = 30 2 · 15 = 30 6 15 2 5 =

  7. You can use the cross product rule to solve proportions with variables.

  8. Example 1: Solving Proportions Using Cross Products Use cross products to solve the proportion. 9 15 m 5 The cross products are equal. = 15 · m = 9 · 5 Multiply. 15m = 45 15m 15 = Divide each side by 15. 45 15 m = 3

  9. Check It Out! Example 2 Use cross products to solve the proportion. 6 7 m 14 The cross products are equal. = 7 · m = 6 · 14 Multiply. 7m = 84 Divide each side by 7 to isolate the variable. 7m 7 84 7 = m = 12

  10. Check It Out! Example 3 Use cross products to solve the proportion. 7 84 12 h The cross products are equal. = 7 · h = 84 · 12 Multiply. 7h = 1008 Divide each side by 7 to isolate the variable. 7h 7 1008 7 = m = 144

  11. Check It Out! Example 4 Use cross products to solve the proportion. 5 140 12 v The cross products are equal. = 5 · v = 140 · 12 Multiply. 5v = 1680 Divide each side by 5 to isolate the variable. 5v 5 1680 5 = v = 336

  12. Check It Out! Example 5 Use cross products to solve the proportion. 1.2 n 8 12 The cross products are equal. = 1.2 · 12= 8 · n Multiply. 14.4= 8n Divide each side by 8 to isolate the variable. 14.4 8 8n 8 = 1.8= n

  13. Check It Out! Example 6 Use cross products to solve the proportion. n 9.3 6 8 The cross products are equal. = 8 · n = 9.3 · 6 Multiply. 8n = 55.8 Divide each side by 8 to isolate the variable. 8n 8 55.8 8 = n = 6.975

  14. It is important to set up proportions correctly. Each ratio must compare corresponding quantities in the same order. 16 mi 4 hr 8 mi x hr 16 mi 8 mi 4 hr xhr = = 16 mi 4 hr 8 hr x mi =

  15. Example 9: Problem-Solving Application A piglet can gain 3 pounds in 36 hours. If this rate continues, when will the piglet reach 18 pounds?

  16. Example 10: Problem-Solving Application S. Petey drives 130 miles every two hours. If this rate continues, how long will it take her to drive 1,000 miles?

  17. Example 11: Problem-Solving Application The ratio of dogs to cats at a kennel is exactly 4 to 5. If there are 36 dogs at the kennel, how many cats are at the kennel?

  18. Example 12: Problem-Solving Application Pho Toeh reduced a print that was 9 inches wide and 15 inches long. If the width of the reduction is 3 inches, what is the length?

  19. Home Learning On-Line Tutoring

  20. x 9 19 57 = 2. Lesson Quiz Use cross products to solve each proportion. 45 t 25 20 1. = t = 36 x = 3 2 3 r 36 n 10 28 8 = n = 35 3. r = 24 4. = 5. Carmen bought 3 pounds of bananas for $1.08. June paid $ 1.80 for her purchase of bananas. If they paid the same price per pound, how many pounds did June buy? 5 pounds

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