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Solving proportions

Learn how to solve proportions, use ratios effectively, and work with similar figures in geometry. Practice solving proportions with step-by-step examples and check your solutions. Explore the concept of similarity and apply the cross products property to find missing values.

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Solving proportions

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  1. Solving proportions

  2. 1 4 = 1:3 = 3:9 2 8 Proportions What are proportions? - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures. What do we mean by similar? - Similar describes things which have the same shape but are not the same size.

  3. 7 = 16 t 32 = 18 b 24 12 Solve the proportion. 14 ANSWER 9 ANSWER

  4. What if….. • Sometimes the equivalent ratios are not simple.

  5. Cross multiply

  6. Cross multiply

  7. Cross multiply

  8. Set up and solve this proportion. 8) 5 is to 4 as 45 is to x. 5 45 Now cross multiply ____ = ____ x 4 = 180 5x 5 5 36 x =

  9. First - Set up & solve the proportion. 9) 3 is to 2 as x is to 18. 3 x Now cross multiply ____ = ____ 18 2 = 54 2x 2 2 x = 27

  10. NO set up this time!! Just solve….. 10) 6x 144 = 6 6 x 24 =

  11. Solve the proportion = . 8 6 6 8 x 15 15 x = 8 15 = x 6 Use the cross products property Write original proportion. Cross products property 120 = 6x Simplify. 20=x Divide each side by 6.

  12. 4 a 5 = 37 ANSWER 29.6 EXAMPLE 1 GUIDED PRACTICE Solve the proportion. Check your solution.

  13. 21 2 = n 5 4 9 = p 11 Solve the proportion. 52.5 ANSWER 24.75 ANSWER

  14. 4 15 = 7 x 5 2 = p 32 Solve the proportion. 26.25 ANSWER 12.8 ANSWER

  15. Solve the proportion. It takes 30 tomatillos to make 8 ounces of enchilada sauce. How many tomatillos does it take to make 12 ounces of enchilada sauce? SET IT UP

  16. 30 x = 8 12 Solve the proportion. It takes 30 tomatillos to make 8 ounces of enchilada sauce. How many tomatillos does it take to make 12 ounces of enchilada sauce? SET IT UP

  17. Solve the proportion. It takes 30 tomatillos to make 8 ounces of enchilada sauce. How many tomatillos does it take to make 12 ounces of enchilada sauce? 45 tomatillos ANSWER

  18. a 7 9 = 21 ANSWER 3 Solve the proportion.

  19. = 16 ANSWER 32 m x A printer can print 12 color pages in 3 minutes. How many color pages can the printer print in 9 minutes? Write and solve a proportion to find the answer. 28 14 9 ANSWER ; 36 color pages = 12 3 Solve the proportion.

  20. Seals Each day, the seals at an aquarium are each fed 8 pounds of food for every 100 pounds of their body weight. A seal at the aquarium weighs 280 pounds. How much food should the seal be fed per day? SOLUTION STEP 1 Write a proportion involving two ratios that compare the amount of food with the weight of the seal. x 280 8 amount of food = weight of seal 100

  21. Maps SOLUTION From the map’s scale, 1 centimeter represents 85 kilometers. On the map, the distance between Cleveland and Cincinnati is about 4.2 centimeters. Use the scale on a map

  22. 1 centimeters = 85 kilometers 1 d = 85 4.2 ANSWER 4.2 The actual distance between Cleveland and Cincinnati is about 357 kilometers. d Write and solve a proportion to find the distance d between the cities. Cross products property d = 357 Simplify.

  23. 6. The ship model kits sold at a hobby store have a scale of 1 ft : 600 ft. A completed model of the Queen Elizabeth II is 1.6 feet long. Estimate the actual length of the Queen Elizabeth II. ANSWER about 960 ft Use the scale on a map EXAMPLE 4 GUIDED PRACTICE Model ships

  24. Solving Proportional Problems So how do we use proportions and similar figures? 8 feet 4 feet 2 feet ? feet

  25. Solving Proportional Problems So how do we use proportions and similar figures? ANSWER 4 8 feet 4 feet 2 feet ? feet

  26. Try One Yourself Set up a proportion. What is the width of the larger stick figure? 8 feet 12 feet 4 feet x feet

  27. 48 ft x ft = 3 ft 4 ft Solving for the Building’s Height building Here is a sample calculation for the height of a building: x feet 48 feet 4x = 144 x = 36 yardstick 3 feet The height of the building is 36 feet. 4 feet

  28. You try it!! 11) Now simplify 16m 8 = 16 16 m =

  29. 12) Mr. Jones has taken a survey of college students and found that 40 out of 47 students are liberal arts majors. If a college has 10,827 students, what is the number of students who are liberal arts majors, rounded to the nearest whole number? First – Set up Your proportion! x 40 ____ = _______ 10,827 47 433,080 47x = Now cross multiply 47 47 x = 9214

  30. 13) Geothermal energy is heat from inside the earth. Underground temperatures generally increase 9°C for every 300 meters of depth. How deep would a well have to be for the temperature to reach 216°C ? First – Set up Your proportion! 9° 216° ____ = _____ m 300 = 64800 9m 9 9 m = 7200

  31. 14) A map has a scale of 1 cm = 30 km. If two cities are 11 cm apart on the map, what is the actual distance between the two cities to the nearest tenth of a km? First – Set up Your proportion! 11cm 1cm ____ = _____ x 30km 330 1x = x 330 km =

  32. Practice

  33. Practice

  34. Practice

  35. Practice

  36. Practice

  37. Practice

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