7 -3 Proportions Warm Up Problem of the

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

7 -3 Proportions Warm Up Use the table to write each ratio. Brown bears Giraffes Monkeys Polar Bears 1. 2. 3. 4. 3 2 17 4 giraffes to monkeys polar bears to all bears monkeys to all animals to all bears 2: 17 4: 7 17: 26 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 Florida State Standards FSMA. 6. A. 2. 2 …Compare ratios and rates. Also FSMA. 6. A. 3. 2

7 -3 Proportions Vocabulary proportion

7 -3 Proportions A proportion is an equation that shows two equivalent ratios. 2 4 __ __ = 1 2 4 8 __ __ = 2 4 2 6 __ __ = 1 3 Reading Math 2 4 __ = __ as “two is to Read the proportion 1 2 one as four is to two. ”

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

7 -3 Proportions Check It Out : Example 1 A 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 = x 3 9 x = 15 X 3 = $45

7 -3 Proportions Check It Out : Example 1 B 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? 120 = x 2 6 x = 120 X 3 = 360 miles

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

7 -3 Proportions Additional Example 2 A: Using Cross Products to Complete Proportions Find the missing value in the proportion. 5 n __ __ = 6 18 6 • n = 5 • 18 6 n = 90 90 6 n ___ = ___ 6 6 n = 15 Find the cross products. The cross products are equal. n is multiplied by 6. Divide both sides by 6 to undo the multiplication.

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

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

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

7 -3 Proportions Check It Out: Example 2 C Find the missing value in each proportion. 2 6 __ = __ 13 n 2 • n = 6 • 13 2 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? 1 tbsp f _____ = ____ 6 gal 4 gal Let f be the amount of fertilizer for 4 gallons of water. 1 tbsp f _____ = ____ 6 gal 4 gal Write a proportion. 6 • f =1 • 4 The cross products are equal.

7 -3 Proportions Caution! In a proportion, the units must be in the same order in both ratios. tbsp ___ = ___ gal gal ___ = ___ or tbsp

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

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? 8 __ 3 = n __ 15 3 • n =8 3 • n = 120 • 15 n = 40 gallons

7 -3 Proportions Lesson Quizzes Standard Lesson Quiz for Student Response Systems

7 -3 Proportions Lesson Quiz 1. Angelo bought 4 songs online for $2. How much would Angelo pay for 12 songs? $6 Find the missing value in each proportion. 9 45 p 5 2. __ = __ 3. __ = __ 5 x 36 6 p = 30 x = 25 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? 9 g

7 -3 Proportions Lesson Quiz for Student Response Systems 1. Rudy spent $15 on 3 CDs at a store where all CDs are the same price. How much would it cost for Rudy to buy 12 CDs? A. $50 B. $45 C. $60 D. $75

7 -3 Proportions Lesson Quiz for Student Response Systems 2. Identify the missing value in the proportion. A. x = 168 B. x = 56 C. x = 72 D. x = 49

7 -3 Proportions Lesson Quiz for Student Response Systems 3. Identify the missing value in the proportion. A. n = 6 B. n = 51 C. n = 34 D. n = 102

7 -3 Proportions Lesson Quiz for Student Response Systems 4. According to the label, 1 tablespoon of mixed fruit concentrate should be used to prepare 200 ml of juice. How many tablespoons of concentrate would you use to prepare 800 ml of juice? A. 2 tbsp B. 3 tbsp C. 4 tbsp D. 5 tbsp