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Use the LCM to rename these ratios with a common denominator.

3 6. 4 6. ,. 1 2. 2 3. Exercise. Use the LCM to rename these ratios with a common denominator. and. 10 15. 9 15. ,. 2 3. 3 5. Exercise. Use the LCM to rename these ratios with a common denominator. and. 20 60. 24 60. 45 60. ,. ,. 3 4. 2 5. 1 3. Exercise.

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Use the LCM to rename these ratios with a common denominator.

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  1. 36 46 , 12 23 Exercise Use the LCM to rename these ratios with a common denominator. and

  2. 1015 915 , 23 35 Exercise Use the LCM to rename these ratios with a common denominator. and

  3. 2060 2460 4560 , , 34 25 13 Exercise Use the LCM to rename these ratios with a common denominator. , , and

  4. 615 410 , 25 Exercise Change these ratios to equivalent ratios by multiplying by 1 in the form of 2 over 2 and 3 over 3.

  5. 129 86 , 43 Exercise Change these ratios to equivalent ratios by multiplying by 1 in the form of 2 over 2 and 3 over 3.

  6. Proportion A proportion is a statement of equality between two ratios.

  7. 1st 3rd 912 68 2nd 4th = The 1st and 4th are called the extremes. The 2nd and 3rd are called the means.

  8. Property of Proportions The product of the extremes is equal to the product of the means.

  9. = = 912 912 129 68 68 86 = also

  10. = = 912 912 128 68 68 96 = also

  11. = = 912 912 812 68 68 69 = also

  12. 35 2012 53 520 312 = = 1220 Example 1 Given = , write a proportion by inversion of ratios and a proportion by alternation of terms.

  13. 8n 615 1206 6n6 = = 8n 615 Example 2 Solve = for n. n = 20 6n = 15 • 8 6n = 120

  14. 10827 32x 864108 108x108 = = 32x Example 3 10827 Solve = for x. x = 8 108x = 32(27) 108x = 864

  15. 72 Example 4x x≈1.14 Solve = .

  16. Example x8 950 x = 1.44 Solve = .

  17. 562 27 8n 2n2 = = Example 4 The ratio of adults to students on a bus is 2 to 7. If there are 8 adults, how many students are on the bus? 2n = 56 n = 28 students

  18. 200 ft.x ft. 3 hr.5 hr. 3x3 1,0003 = = Example 5 Sam can paint 200 ft. of privacy fence in 3 hr. To the nearest foot, how many feet can he paint in 5 hr.? 3x = 200(5) x≈ 333 ft. 3x = 1,000

  19. Example A rectangle whose width is 5 ft. and whose length is 12 ft. is similar to a rectangle whose width is 8 ft. What is the length of the larger rectangle? 19.2 ft.

  20. Example What is the height of a tree if a 6 ft. man standing next to the tree makes an 8 ft. shadow and the tree makes a 50 ft. shadow? 37.5 ft.

  21. Example If a car can go 250 mi. on 8 gal., how many gallons will it take to go on a 600 mi. trip? 19.2 gal.

  22. Example If a 50 ft. fence requires 84 2” x 4”s, how many 2” x 4”s are needed for a 160 ft. fence? 269

  23. Example The product of ratios is also a ratio. For example, suppose a production line can assemble 130 cars per hour. How many days, at 8 hr./day, will it take to produce 100,000 cars? 97 days

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