1. 7-4 Proportions I CAN write and solve proportions.

2. 7-4 Proportions Vocabulary proportion

3. 7-4 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

4. 7-4 Proportions 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.

5. 7-4 Proportions 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

6. 7-4 Proportions You Try! 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.

7. 7-4 Proportions You Try! 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

8. 7-4 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

9. 7-4 Proportions 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

10. 7-4 Proportions You Try! 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

11. 7-4 Proportions 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. f 4 gal ____ 1 tbsp 6 gal _____ = 6 f = 1 4The cross products are equal.

12. 7-4 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

13. 7-4 Proportions 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 __

14. 7-4 Proportions You Try! Example 3 According to the label, 3 tablespoons of plant fertilizer should be used per 7 gallons of water. How many tablespoons of fertilizer would you use for 2 gallons of water? f 2 gal ____ 3 tbsp 7 gal _____ = Let f be the amount of fertilizer for 2 gallons of water. f 2 gal ____ 3 tbsp 7 gal _____ = Write a proportion. 7 f = 3 2The cross products are equal.

15. 7-4 Proportions You Try! Example 3 Continued f is multiplied by 7. Divide both side by 7 to undo the multiplication. Write your answer in simplest form. 7f = 6 7f7f 7 ___ 6 7 __ = f = tbsp 6 7 __ You would use tbsp of fertilizer for 2 gallons of water. 6 7 __

16. 7-4 Proportions CAN YOU write and solve proportions?

17. 7-4 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

18. 7-4 Proportions HOMEWORK p. 304: 1-12, 14-20 even, 22, 23