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Proportions Practice for Math Learners | Helpful Lesson Presentation

This presentation covers ratios, proportions, cross products, and applying proportions in real-life scenarios in an interactive manner. Build your math skills and boost problem-solving capabilities.

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Proportions Practice for Math Learners | Helpful Lesson Presentation

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

  2. Brown bears 3 Giraffes 2 Monkeys 17 Polar Bears 4 Warm Up Use the table to write each ratio. 1. giraffes to monkeys 2. polar bears to all bears 3. monkeys to all animals 4. all animals to all bears 2:17 4:7 17:26 26:7

  3. Problem of the Day A carpenter can build one doghouse in one day. How many doghouses can 12 carpenters build in 20 days? 240

  4. Learn to write and solve proportions.

  5. Vocabulary proportion

  6. 2 4 4 8 2 6 __ __ __ __ __ __ = = = 1 2 2 4 1 3 2 4 __ __ 1 2 A proportion is an equation that shows two equivalent ratios. Reading Math Read the proportion = as “two is to one as four is to two.”

  7. 4 number of hearts __ number of stars 8 Additional Example 1: Modeling Proportions Write a proportion for the model. First write the ratio of hearts to stars. = Next separate the hearts and stars into two equal groups.

  8. 2 __ number of hearts number of stars 4 4 2 __ __ 8 4 Additional Example 1 Continued Now write the ratio of hearts to stars in each group. = A proportion shown by the model is = .

  9. 2 number of faces __ number of moons 6 Check It Out: Example 1 Write a proportion for the model. First write the ratio of faces to moons. = Next separate the faces and moons into two equal groups.

  10. 1 __ number of faces number of moons 3 2 1 __ __ 6 3 Check It Out: Example 1 Continued Now write the ratio of faces to moons in each group. = A proportion shown by the model is = .

  11. CROSS PRODUCTS Cross products in proportions are equal 4 2 3 9 9 3 14 2 __ __ __ ___ __ __ __ __ = = = = 8 4 5 15 6 2 7 1 6 •3 = 9 • 2 7 •2 = 14 • 1 8 • 2 = 4 • 4 5 • 9 = 3 • 15 16= 16 18 = 18 14 = 14 45= 45

  12. 5 n __ __ = 6 18 90 6n ___ ___ 6 6 Additional Example 2: Using Cross Products to Complete Proportions Find the missing value in the proportion. Find the cross products. 6 •n= The cross products are equal. 5 • 18 6n= 90 n is multiplied by 6. Divide both sides by 6 to undo the multiplication. = n = 15

  13. 3 n __ __ = 5 15 45 5n ___ ___ 5 5 Check It Out: Example 2 Find the missing value in the proportion. Find the cross products. 5 •n= The cross products are equal. 3 • 15 5n= 45 n is multiplied by 5. Divide both sides by 5 to undo the multiplication. = n = 9

  14. 1 tbsp f _____ ____ 6 gal 4 gal 1 tbsp f _____ ____ 6 gal 4 gal Additional Example 3: Measurement Application According to the label, 1 tablespoon of plant fertilizer should be used per 6 gallons of water. How many tablespoons of fertilizer would you use for 4 gallons of water? Let f be the amount of fertilizer for 4 gallons of water. = = Write a proportion. 6 •f= 1 • 4 The cross products are equal.

  15. tbsp tbsp ___ ___ gal gal gal gal ___ ___ tbsp tbsp Caution! In a proportion, the units must be in the same order in both ratios. = or =

  16. 4 6f __ ___ 6 6 2 __ 3 2 __ 3 Additional Example 3 Continued f is multiplied by 6. 6f= 4 Divide both sides by 6 to undo the multiplication. = Write your answer in simplest form. f = tbsp You would use tbsp of fertilizer for 4 gallons of water.

  17. 3 tbsp f _____ ____ 9 gal 2 gal 3 tbsp f _____ ____ 9 gal 2 gal Check It Out: Example 3 According to the label, 3 tablespoons of plant fertilizer should be used per 9 gallons of water. How many tablespoons of fertilizer would you use for 2 gallons of water? Let f be the amount of fertilizer for 2 gallons of water. = = Write a proportion. 9 •f= 3 • 2 The cross products are equal.

  18. 6 9f __ ___ 9 9 2 __ 3 2 __ 3 Check It Out: Example 3 Continued f is multiplied by 9. 9f= 6 Divide both side by 9 to undo the multiplication. = Write your answer in simplest form. f = tbsp You would use tbsp of fertilizer for 2 gallons of water.

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

  20. 2 1 __ __ 6 3 9 45 p 5 __ __ __ __ 5 x 36 6 Lesson Quiz 1. Write a proportion for the model. Find the missing value in each proportion. 2. = 3. = 4. The label on a bottle of salad dressing states that there are 3 grams of fat per tablespoon. If you use 3 tablespoons, how many grams of fat would you be getting? = x = 25 p = 30 9 g

  21. Lesson Quiz for Student Response Systems 1. Identify a proportion for the model. A. B. C. D.

  22. Lesson Quiz for Student Response Systems 2. Identify the missing value in the proportion. A. x = 168 B. x = 56 C. x = 72 D. x = 49

  23. Lesson Quiz for Student Response Systems 3. Identify the missing value in the proportion. A. n = 6 B. n = 51 C. n = 34 D. n = 102

  24. Lesson Quiz for Student Response Systems 4. According to the label, 1 tablespoon of mixed fruit concentrate should be used to prepare 200 ml of juice. How many tablespoons of concentrate would you use to prepare 800 ml of juice? A. 2 tbspB. 3 tbsp C. 4 tbspD. 5 tbsp

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