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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. Warm Up. Determine whether the ratios are proportional. 5 8. 15 24. ,. 1. yes. 16 25. 12 15. ,. 2. no. 15 10. 20 16. ,. 3. no. 14 18. 42 54. ,. yes. 4. Problem of the Day

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. Warm Up Determine whether the ratios are proportional. 5 8 15 24 , 1. yes 16 25 12 15 , 2. no 15 10 20 16 , 3. no 14 18 42 54 , yes 4.

  3. Problem of the Day If A = 1, B = 2, C = 3, D = 4, and so on, all the way to Z = 26, then what is A + B + C + D + . . . + Z = ?(Hint: A + Z = B + Y.)‏ 351

  4. Sunshine State Standards MA.7.A.1.1 …Use proportions to solve problems. Also MA.7.A.1.6

  5. Vocabulary cross product: the product of the numerator in one ratio and the denominator in the other

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

  7. You can use cross products to solve proportions with variables.

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

  9. 9 6 6 7 m 14 r 7 = = Check It Out: Example 1 Use cross products to solve the proportion. A. 84 7 12 6·14 = 7m;m = = B. 63 6 10.5 9·7 = 6r;r = =

  10. It is important to set up proportions correctly. Each ratio must compare corresponding quantities in the same order. Suppose a boat travels 16 miles in 4 hours and 8 miles in x hours at the same speed. Either of these proportions could represent this situation. 16 mi 4 hr 8 mi x hr 16 mi 8 mi 4 hr xhr = =

  11. 1 Understand the Problem Additional Example 2:Problem Solving Application If 3 binders of the same size take up 4 inches of space on a shelf, how much space will be needed for all 26 of these binders? Rewrite the question as a statement. • Find the space needed for 26 binders. List the important information: • 3 binders take up 4 inches of space.

  12. 2 Make a Plan Additional Example 2 Continued Set up a proportion using the given information. Let x represent the inches of space needed. binders inches 3 binders 4 inches 26 binders x =

  13. 3 Solve Additional Example 2 Continued 3 4 26 x Write the proportion. = 3 · x = 4 · 26 The cross products are equal. 3x = 104 Multiply. Divide each side by 3 to isolate the variable. 3x 3 104 3 = 2 3 x = 34 2 3 She needs 34 inches for all 26 binders.

  14. 4 Additional Example 2 Continued Look Back 4 · 26 = 104 26 3 4 = 2 3 34 2 3 = 104 3 · 34 2 3 is the The cross products are equal, so 34 answer

  15. Check It Out: Example 2A A stack of 33 CDs is 1.5 inches high. How many CDs would be in a stack that is 3.5 inches high? 1.5 33 3.5 x = 1·5x = 33 x 3.5 115.5 1.5 x = x = 77 CDs

  16. Check It Out: Example 2B Maria drives at a constant speed for 3 hours and travels 175 miles. How far would she drive in 4.5 hours at the same speed? 3 175 4.5 x = 3x = 175 . 4.5 787.5 3 x = x = 262.5 miles

  17. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  18. x 9 19 57 = 2. Lesson Quiz: Part I Use cross products to solve the proportion. 45 t 25 20 1. = t = 36 x = 3 2 3 r 36 = 3. r = 24 n 10 28 8 n = 35 4. =

  19. Lesson Quiz: Part II 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

  20. Lesson Quiz for Student Response Systems 1. Use cross products to solve the proportion. = A.t = 16 B.t = 24 C.t = 32 D.t = 36 24 16 48 t

  21. Lesson Quiz for Student Response Systems 2. Use cross products to solve the proportion. = A.y = 2 B.y = 4 C.y = 8 D.y = 16 y16 21 84

  22. Lesson Quiz for Student Response Systems 3. Use cross products to solve the proportion. = A.r = 20 B.r = 15 C.r = 10 D.r = 5 4 5 r25

  23. Lesson Quiz for Student Response Systems 4. Use cross products to solve the proportion. = A.n = 21 B.n = 28 C.n = 32 D.n = 36 n16 21 12

  24. Lesson Quiz for Student Response Systems 5. If you put an object that has a mass of 25 grams on one side of the balance scale, you would have to put 55 paper clips on the other side to balance the weight. How many paper clips would balance the weight of a 30-gram object? A. 55 paper clips B. 58 paper clips C. 60 paper clips D. 66 paper clips

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