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Warm Up

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

christophe-alden
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Warm Up

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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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