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

Use the table to write each ratio. 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 Brown bears 3 Giraffes 2 Monkeys 17 Polar Bears 4 2:17 4:7 17:26 26:7

Problem of the Day A carpenter can build one doghouse in one day. How many doghouses can 12 carpenters build in 20 days? 240

Learn to write and solve proportions.

Vocabulary proportion

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

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

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

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

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 __ = 2 6 __ 1 3 __ A proportion shown by the model is = .

Cross products in proportions are equal 4 8 __ 2 = 3 5 __ 9 15 ___ = 9 6 __ 3 2 = 14 7 __ 2 1 = 8 • 2 = 4 • 4 5 • 9 = 3 • 15 6 • 3 = 9 • 2 7 • 2 = 14 • 1 16 = 16 45 = 45 18 = 18 14 = 14

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

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

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

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

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

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

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

1. Write a proportion for the model. 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? 2 6 __ 1 3 __ = 9 5 __ 45 x __ p 36 __ 5 6 __ x = 25 p = 30 9 g