1. 7-3 Proportions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 7-3 Proportions 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 4Polar Bears 17Monkeys 2Giraffes 3Brown bears 26:7

3. 7-3 Proportions 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. 7-3 Proportions Learn to write and solve proportions.

5. 7-3 Proportions Vocabulary proportion

6. 7-3 Proportions A proportion is an equation that shows two equivalent ratios. Read the proportion = as “two is to one as four is to two.” 2 1 __ 4 2 = 4 2 8 4 = 2 1 6 3 = 2 1 4 2 Reading Math

7. 7-3 Proportions Additional Example 1: Modeling Proportions Write a proportion for the model. number of hearts number of stars 4 8 __ = First write the ratio of hearts to stars. Next separate the hearts and stars into two equal groups.

8. 7-3 Proportions Additional Example 1 Continued Now write the ratio of hearts to stars in each group. number of hearts number of stars 2 4 __ = A proportion shown by the model is =. 4 8 __ 2 4

9. 7-3 Proportions Check It Out: Example 1 Write a proportion for the model. number of faces number of moons 2 6 __ = First write the ratio of faces to moons. Next separate the faces and moons into two equal groups.

10. 7-3 Proportions Check It Out: Example 1 Continued Now write the ratio of faces to moons in each group. number of faces number of moons 1 3 __ = A proportion shown by the model is =. 2 6 __ 1 3

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

12. 7-3 Proportions Additional Example 2: Using Cross Products to Complete Proportions Find the missing value in the proportion. 6n6n 6 ___ 5 6 __ n 18 __ = Find the cross products. 6 n = 5 18 The cross products are equal. 6n = 90n is multiplied by 6. 90 6 ___ = Divide both sides by 6 to undo the multiplication. n = 15

13. 7-3 Proportions Check It Out: Example 2 Find the missing value in the proportion. 5n5n 5 ___ 3 5 __ n 15 __ = Find the cross products. 5 n = 3 15 The cross products are equal. 5n = 45n is multiplied by 5. 45 5 ___ = Divide both sides by 5 to undo the multiplication. n = 9

14. 7-3 Proportions 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? f 4 gal ____ 1 tbsp 6 gal _____ = Let f be the amount of fertilizer for 4 gallons of water. f 4 gal ____ 1 tbsp 6 gal _____ = Write a proportion. 6 f = 1 4The cross products are equal.

15. 7-3 Proportions In a proportion, the units must be in the same order in both ratios. Caution! tbsp gal ___ tbsp gal ___ = gal tbsp ___ gal tbsp ___ = or

16. 7-3 Proportions Additional Example 3 Continued f is multiplied by 6. Divide both sides by 6 to undo the multiplication. Write your answer in simplest form. 6f = 4 6f6f 6 ___ 4 6 __ = f = tbsp 2 3 __ You would use tbsp of fertilizer for 4 gallons of water. 2 3 __

17. 7-3 Proportions 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? f 2 gal ____ 3 tbsp 9 gal _____ = Let f be the amount of fertilizer for 2 gallons of water. f 2 gal ____ 3 tbsp 9 gal _____ = Write a proportion. 9 f = 3 2The cross products are equal.

18. 7-3 Proportions Check It Out: Example 3 Continued f is multiplied by 9. Divide both side by 9 to undo the multiplication. Write your answer in simplest form. 9f = 6 9f9f 9 ___ 6 9 __ = f = tbsp 2 3 __ You would use tbsp of fertilizer for 2 gallons of water. 2 3 __

19. 7-3 Proportions Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

20. 7-3 Proportions 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? p = 30x = 25 9 g 2 6 __ 1 3 = 9 5 45 x __ p 36 __ 5 6

21. 7-3 Proportions 1. Identify a proportion for the model. A. B. C. D. Lesson Quiz for Student Response Systems

22. 7-3 Proportions 2. Identify the missing value in the proportion. A. x = 168 B. x = 56 C. x = 72 D. x = 49 Lesson Quiz for Student Response Systems

23. 7-3 Proportions 3. Identify the missing value in the proportion. A. n = 6 B. n = 51 C. n = 34 D. n = 102 Lesson Quiz for Student Response Systems

24. 7-3 Proportions 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 tbsp B. 3 tbsp C. 4 tbsp D. 5 tbsp Lesson Quiz for Student Response Systems