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Understanding Proportions: Solving for Missing Values and Real-World Applications

This PowerPoint presentation by Mrs. Mary Angel Alim-Flores focuses on teaching students how to solve for missing values in proportions and address word problems using cross-products. It covers definitions, methods of writing proportions, and step-by-step examples to reinforce understanding. Students will engage with practical scenarios, such as swimming distances and travel times, to see the application of proportions in everyday life. By the end, learners will confidently apply these concepts to solve various problems involving ratios and proportions.

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Understanding Proportions: Solving for Missing Values and Real-World Applications

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  1. Objective 12/09/09 The students will be able to solve for the missing value in a proportion and solve word problems by using cross-products.

  2. A PowerPoint Presentation by Mrs. Mary Angel Alim- Flores Proportions

  3. Making Iced Tea

  4. Making Iced Tea

  5. Making Iced Tea

  6. Making Iced Tea

  7. Making Iced Tea

  8. Making Iced Tea

  9. Two equal ratios form a PROPORTION. Ex. 5 : 10 = 20 : 40 56 = 7 64 8

  10. 2 Ways of Writing a Proportion 1. Colon Form 3:4 = 12: 16 2. Fraction Form 3 = 12 4 16

  11. Extremes 16: 8 = 20:40 Means

  12. To check if two ratios are equal or not: Fraction form • Use cross-products Ex. 3 = 15 4 20 (3x20=60) (4x15=60) Therefore, the two ratios form a proportion.

  13. 2. Colon form Check if the product of the means and product of the extremes are equal. Ex. 4: 6 _____ 12: 18 (6x12= 72) (18x4= 72) Therefore, the two ratios are equal.

  14. To solve for the missing value. • Use cross products 5 = 60 10 x

  15. 5 = 6010 x 1st Step: 5(x)= 5x 2nd Step: 10 (60)= 600 3rd Step: 5x = 600 5 5 Answer: x= 120

  16. 12:36 = 3: m 1st Step: 12 (m)= 12m 2nd Step: 36 (3)= 108 3rd Step: 12m = 108 12 12 Answer: m= 9

  17. Solving Word Problems Grace and James are on a swimming team. Their swim training is 200 meters and usually takes them 3 minutes. How long, at this rate, would it take them to complete an 800-meter swim?

  18. 1. Set up the proportion: meters200 = 800 minutes 3 n 2. Use cross-products 200(n)= 200 n then 3(800)= 2400. 3. Divide both sides by 200 n=12 Answer: 800-meter swim will take them 12 minutes.

  19. A car travels 125 miles in 3 hours. How far would it travel in 5 hours?

  20. A car travels 125 miles in 3 hours. How far would it travel in 5 hours? Step 1 Set up the proportion. miles 125 = h hours 3 5 Step 2 Solve for the missing value (h). 125(5) = 625 then, 3(h)=3h Step 3 Divide both 625 and 3h by 3 Answer: 208.33 or 208 1/3 miles

  21. RECAP Today I learned… The steps in solving proportions are…

  22. Trip Around the World • 1. U.S.A • 2. Philippines • 3. Australia • 4. Canada • 5. Japan

  23. EXIT TICKET A 380- cubic cm sample of titanium has a mass of 1710 g. Find the weight of a titanium sample that has a volume of 532 cubic cm. Explain how you got your answer.

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