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

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

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

7-3 Proportions MA.6.A.2.2 …Compare ratios and rates. Also MA.6.A.3.2 Sunshine State Standards

7-3 Proportions Vocabulary proportion

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 = = = Reading Math

7-3 Proportions Additional Example 1A: Modeling Proportions Julio spent $10 to buy 4 books at a garage sale. How much would Julio pay for 8 books at the garage sale? x = $10  2 = $20 The cost for 8 books at the garage sale is $20. $10 4 ___ x 8 = Write a proportion that compares total cost to number of books. $10 4 ___ x 8 = 22 22 Think: 4  2 = 8 and $10  2 = x.

7-3 Proportions Check It Out : Example 1A Paul spent $15 on 3 CDs at a store where all CDs are the same price. How much would it cost for Paul to buy 9 CDs? $15 3 = x 9 x = 15 X 3 = $45

7-3 Proportions Check It Out : Example 1B Beth drove 120 miles in 2 hours. She continues driving at the same rate and does not stop. How far will she have driven in 6 hours? = x 6 x = 120 X 3 = 360 miles

7-3 Proportions Cross products in proportions are equal CROSS PRODUCTS 3 5 __ 9 15 ___ = 4 8 __ 2 4 = = 14 7 __ 2 1 = 8 2 =4 5 9 = = = = = = = 14

7-3 Proportions Additional Example 2A: 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 ___ = Divide both sides by 6 to undo the multiplication. n = 15

7-3 Proportions Additional Example 2B: Using Cross Products to Complete Proportions Find the missing value in the proportion ___ 3 9 __ 4 n = Find the cross products. 9 4 = 3 n The cross products are equal. 36 = 3nn is multiplied by 3. 3n3n 3 ___ = Divide both sides by 3 to undo the multiplication. n = 12

7-3 Proportions Check It Out: Example 2A Find the missing value in each proportion. 3 5 __ n 15 __ = 5 n = n = 45 n = 9

7-3 Proportions Check It Out: Example 2B Find the missing value in each proportion. 4 9 __ n 27 __ = 9 n = n = 108 n = 12

7-3 Proportions Check It Out: Example 2C Find the missing value in each proportion __ 6 n = 2 n = n = 78 n = 39

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.

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

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 __

7-3 Proportions Check It Out: Example 3 To make a certain shade of pink paint, mix 8 gallons of white paint with 3 gallons of red paint. How many gallons of white paint would you mix with 15 gallons of red paint to make this shade of pink? n 15 __ 8 3 = 3 n = n = 120 n = 40 gallons