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7-3

7-3. Proportions – Using Cross Product. Course 1. Warm Up. Problem of the Day. Lesson Presentation. 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.

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7-3

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  1. 7-3 Proportions – Using Cross Product Course 1 Warm Up Problem of the Day Lesson Presentation

  2. 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. 4 2 2 6 4 2 4 8 __ __ __ __ __ __ __ __ = = = 4 1 2 1 1 2 2 3 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.”

  6. Vocabulary proportion

  7. 4 __ 8 number of hearts number of stars 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 4 2 __ __ __ 4 8 4 number of hearts number of stars Additional Example 1 Continued Now write the ratio of hearts to stars in each group. = A proportion shown by the model is = .

  9. 2 __ 6 number of faces number of moons 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 2 1 __ __ __ 3 6 3 number of faces number of moons 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. 5 6n 90 n __ __ ___ ___ = 6 18 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

  12. = 2 3 4 9 2 9 3 14 __ __ __ __ __ __ __ ___ = = = 2 8 7 6 15 1 4 5 6 •3 = 9 • 2 7 •2 = 14 • 1 8 • 2 = 4 • 4 5 • 9 = 3 • 15 16= 16 18 = 18 14 = 14 45= 45

  13. 3 5n 45 n __ __ ___ ___ = 5 15 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. f f 1 tbsp 1 tbsp ____ _____ _____ ____ 4 gal 6 gal 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 ___ ___ ___ ___ tbsp tbsp gal gal Caution! In a proportion, the units must be in the same order in both ratios. = or =

  16. 2 2 6f 4 __ __ __ ___ 3 6 6 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. f f 3 tbsp 3 tbsp ____ _____ _____ ____ 2 gal 9 gal 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. 2 2 9f 6 __ __ __ ___ 3 9 9 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. 1 5 45 p 2 9 __ __ __ __ __ __ 3 6 6 5 36 x 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

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