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.