1. 8-2 Proportions Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

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 Course 1 8-2 Proportions Brown bears3 Giraffes2 Monkeys17 Polar Bears4 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 Course 1 8-2 Proportions

4. Learn to write and solve proportions. Course 1 8-2 Proportions

5. Vocabulary proportion Insert Lesson Title Here Course 1 8-2 Proportions

6. Course 1 8-2 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

7. Course 1 8-2 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. Course 1 8-2 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. Course 1 8-2 Proportions Try This: 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. Course 1 8-2 Proportions Try This: Example 1 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. Course 1 8-2 Proportions CROSS PRODUCTS Cross products in proportions are equal 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. Course 1 8-2 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. Course 1 8-2 Proportions Try This: 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. Course 1 8-2 Proportions In a proportion, the units must be in the same order in both ratios. Helpful Hint tsp lb ___ tsp lb ___ = lb tsp ___ lb tsp ___ = or

15. Course 1 8-2 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.

16. Course 1 8-2 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. Course 1 8-2 Proportions Try This: 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. Course 1 8-2 Proportions Try This: 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. 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 Insert Lesson Title Here 9 g Course 1 8-2 Proportions 2 6 __ 1 3 = 9 5 45 x __ p 36 __ 5 6