# A ratio is a relationship between two quantities.

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A ratio is a relationship between two quantities.
Learning Objective We will solve1 problems involving proportional relationships. CCSS 7.RP.1 - Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks ½ mile in each ¼ hour, compute the unit rate as the complex fraction ½ / ¼ miles per hour, equivalently 2 miles per hour. What are we going to do? What does solve mean? Solve means __________. CFU Activate Prior Knowledge A ratio is a relationship between two quantities. • A ratio can be written with words or numbers. Write each situation as a ratio. 1. At the park, there are five ducks for every six geese. 5 6 or 5:6 Students, you already know how to write a situation as a ratio. Now, we will use ratios to solve problems involving proportional relationships. Make Connection 2. On a piano, there are five black keys for every seven white keys. 1 find the answer Vocabulary 5 7 or 5:7

On a piano, the ratio of black keys to white keys is 5 to 7.
Concept Development A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. To generate2 an equivalent ratio, multiply or divide each quantity in a ratio by the same number. Multiplying or dividing by the same number does NOT change the ratio. Proportional Relationship On a piano, the ratio of black keys to white keys is 5 to 7. × 2 × 3 × 4 Equivalent Ratios Explain why the ratios are equivalent ratios. In your own words, what is a proportional relationship? A proportional relationship ___________. CFU 5 7 25 35 and black keys 5 10 15 20 25 30 35 white keys 7 14 21 28 42 49 × 4 × 3 × 2 Animated 2 create Vocabulary If there are 20 black keys then there are 28 white keys. If there are 10 black keys then there are 14 white keys. If there are 5 black keys then there are 7 white keys. If there are 15 black keys then there are 21 white keys.

A proportional relationship is a set of equivalent ratios.
Skill Development/Guided Practice A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Read the problem carefully. Identify3 the given ratio. (underline) Identify information about the unknown ratio. (circle) Represent4 the proportional relationship. Hint: Use a table. Generate an equivalent ratio to solve for the unknown. Hint: Multiply or divide by the same value. Interpret5 the solution. Solve problems involving proportional relationships. 1 2 3 4 a b How did I/you identify information about the given ratio? How did I/you identify information about the unknown ratio? How did I/you represent the proportional relationship? How did I/you solve for the unknown? CFU 2 1a 1b 3 1. Neil’s recipe for walnut spice cake calls for two cups of flour for every cup of walnuts. If Neil uses six cups of flour, how many cups of walnuts should he use? _____________________________________________ 2. Selena is buying gas at four dollars for every gallon of gas. If Selena spent 16 dollars, how many gallons of gas did she buy? flour walnuts 2 cups 1 cup × 3 × 3 6 cups ? cups 3 cups If Neil uses six cups of flour, he should use 3 cups of walnuts. dollars gallons \$4 1 3 find (synonym) 4 show (synonym) 5 explain (synonym) Vocabulary × 4 × 4 \$16 ? 4 If Selena spent 16 dollars, she bought 4 gallons of gas.

A proportional relationship is a set of equivalent ratios.
Skill Development/Guided Practice (continued) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Read the problem carefully. Identify the given ratio. (underline) Identify information about the unknown ratio. (circle) Represent the proportional relationship. Hint: Use a table. Generate an equivalent ratio to solve for the unknown. Hint: Multiply or divide by the same value. Interpret the solution. Solve problems involving proportional relationships. 1 2 3 4 a b How did I/you identify information about the given ratio? How did I/you identify information about the unknown ratio? How did I/you represent the proportional relationship? How did I/you solve for the unknown? CFU 2 1a 1b 3 3. A grocery store is selling three melons for seven dollars. If Harold spent \$28 on melons, how many did he buy? _____________________________________________ 4. In Maya’s marble collection, she has three red marbles for every four blue marbles. If Maya has 28 blue marbles, how many red marbles are in her collection? melons dollars 3 7 × 4 × 4 ? 12 28 If Harold spent \$28, he bought 12 melons. red blue 3 4 × 7 × 7 ? 21 If Maya has 28 blue marbles, she has 21 red marbles. 28

A proportional relationship is a set of equivalent ratios.
Skill Development/Guided Practice (continued) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Read the problem carefully. Identify the given ratio. (underline) Identify information about the unknown ratio. (circle) Represent the proportional relationship. Hint: Use a table. Generate an equivalent ratio to solve for the unknown. Hint: Multiply or divide by the same value. Interpret the solution. Solve problems involving proportional relationships. 1 2 3 4 a b How did I/you identify information about the given ratio? How did I/you identify information about the unknown ratio? How did I/you represent the proportional relationship? How did I/you solve for the unknown? CFU 2 1a 1b 3 5. A koi pond has 27 orange fish and 45 white fish. How many orange fish are there for every five white fish? A second koi pond has 20 white fish. If the fish are in the same ratio, how many orange fish are in the second koi pond? _____________________________________________ 6. Monique bought yams at the store. She spent 24 dollars on 18 yams. At this price, how much did Monique pay for every 3 yams? Martin bought yams at the same store and spent 16 dollars. How many yams did Martin buy? orange white 27 45 There are three orange fish for every five white fish.  9  9 3 ? 5  4  4 If there are 20 white fish, there are twelve orange fish. ? 12 20 dollars yams 24 18 Monique paid four dollars for every three yams.  6  6 ? 4 3  4  4 If Martin spent 16 dollars, he bought twelve yams. 16 ? 12

A proportional relationship is a set of equivalent ratios.
Equivalent ratios have equal values using different numbers. Word Bank proportional relationship equivalent ratio generate Skill Closure Read the problem carefully. Identify the given ratio. (underline) Identify information about the unknown ratio. (circle) Represent the proportional relationship. Hint: Use a table. Generate an equivalent ratio to solve for the unknown. Hint: Multiply or divide by the same value. Interpret the solution. Solve problems involving proportional relationships. 1 2 3 4 a b 1. There were four adults for every child in line at the movie theatre. If there were 8 children in line, how many adults were in line at the movie theatre? _____________________________________________ adults children 4 1 × 8 × 8 ? 32 8 If there were 8 children in line, there were 32 adults. Access Common Core Yuri created a table to solve the problem above. Explain the error Yuri made. adults children 4 1 ? 8 Yuri placed the total number of children in line in the wrong column. It should be in the children column. Summary Closure What did you learn today about solving problems involving proportional relationships? (Pair-Share) Use words from the word bank.

A proportional relationship is a set of equivalent ratios.
Independent Practice A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Read the problem carefully. Identify the given ratio. (underline) Identify information about the unknown ratio. (circle) Represent the proportional relationship. Hint: Use a table. Create an equivalent ratio to solve for the unknown. Hint: Multiply or divide by the same value. Interpret the solution. Solve problems involving proportional relationships. 1 2 3 4 a b 1. Jason is cooking rice for his family for dinner. The recipe calls for 2 cups of water for every 1 cup of rice. If he uses 4 cups of water, how much rice should he add? _____________________________________________ 2. Raymond is shopping for produce at the local farmer’s market. A fruit stand sells 4 avocados for \$3. How much will he pay for 20 avocados? water rice 2 cups 1 cup × 2 × 2 4 cups ? cups 2 cups If Jason adds 4 cups of water, he should add 2 cups of rice. avocados dollars 4 3 × 4 × 4 Raymond will pay \$15 for 20 avocados. 20 ? 15

A proportional relationship is a set of equivalent ratios.
Independent Practice (continued) A proportional relationship is a set of equivalent ratios. Equivalent ratios have equal values using different numbers. Read the problem carefully. Identify the given ratio. (underline) Identify information about the unknown ratio. (circle) Represent the proportional relationship. Hint: Use a table. Create an equivalent ratio to solve for the unknown. Hint: Multiply or divide by the same value. Interpret the solution. Solve problems involving proportional relationships. 1 2 3 4 a b 3. In a box, there are 35 pencils and 10 pens. How many pens are there for every seven pencils? Another box has pencils and pens in the same ratio. If there are 20 pens, how many pencils are in the second box? _____________________________________________ pencils pens 35 10  5  5 There are two pens for every seven pencils. 7 ? 2  10  10 If there are 20 pens, there are 70 pencils. ? 70 20

1. 2. 3. If there are 15 adults, there are 75 students.
Periodic Review 1 1. The 6th-grade classes are taking a field trip to the aviary1. There is one adult for every five students. If there are fifteen adults on the field trip, how many students are taking the field trip? _____________________________________________ 2. The aviary has three macaws for every two cockatoos. If there are twelve cockatoos at the aviary, how many macaws are there? adults students 1 5 × 15 × 15 15 ? 75 If there are 15 adults, there are 75 students. macaws cockatoos 3 2 × 6 × 6 ? 18 12 If there are 12 cockatoos, there are 18 macaws. Access Common Core Fill in the missing values for each proportional relationship. Explain how you found the missing values. 12 15 21 1. 3 6 9 18 4 12 16 28 8 20 24 10 12 2. 2 4 6 8 14 5 20 25 10 15 30 35 7 28 42 49 3. 14 21 35 8 16 40 48 56 1 large building or cage for birds Vocabulary 24 32

Twelve inches on the map represents 40 miles.
Periodic Review 2 1. A map of Seattle uses a scale of six inches for every twenty miles. How many miles are represented by twelve inches on the map? _________________________________________ inches miles 6 20 × 2 × 2 12 ? Twelve inches on the map represents 40 miles. 40 Access Common Core 1. Choose Yes or No to indicate whether each ratio is equivalent to . 6 10 O Yes O No A B C 3 5 8 21 35 2. Choose Yes or No to indicate whether each ratio is equivalent to . 5 10 O Yes O No A B C 1 2 15 30 3. Choose Yes or No to indicate whether each ratio is equivalent to . 3 9 O Yes O No A B C 21 63 1 6