MATH SOL 7.4 Rates, Ratios, and Proportions The students will solve singe-step and multi-step practical problems using proportional reasoning.

Table of Contents (Essential Questions) Note Taking Strategies Lesson 1: What is the difference between a rate, a ratio, and a proportion? Lesson 2: How do I determine if two ratios are equivalent? Lesson 3: How do I solve a proportion? Lesson 4: How do I solve a rate? Lesson 5: How do I solve a percent problem? Unit Exam MATH 7.4

Note Taking Strategies 1.) Write each essential question at the top of the next clean page. 2.) When you see this symbol, you must take notes. Write neatly so you can read what you wrote later on. Follow along with the example. 3) Use your notes for help on homework and to study for tests and quizzes! 7.4 : Rates, Ratios, and Proportions

WHAT IS THE DIFFERENCE BETWEEN A RATE, A RATIO, AND A PROPORTION? Unit 4: Rates, Ratios, and Proportions Lesson 1

EQ: What is the difference between a rate, a ratio, and a proportion? Vocabulary Lesson 1 Ratio: a comparison of two numbers or quantities. Can be written as… 1. a fraction “9 out of 10” = 9/10 2. using a colon (:) 3. using the word “to” Any way can be reduced. Part Total EQ: What is the difference between a rate, a ratio, and a proportion?

EQ: What is the difference between a rate, a ratio, and a proportion? Vocabulary Lesson 1 $240 30 hours Rate: A ratio that compares two quantities with different units of measure like: pay rates speed cost Hear the word “per.” 40 Miles 1 hour $3.20 4 pounds EQ: What is the difference between a rate, a ratio, and a proportion?

EQ: What is the difference between a rate, a ratio, and a proportion? Vocabulary Lesson 1 Proportion: An equation that states that two ratios are equivalent. Has means and extremes. 1 2 2 4 = EQ: What is the difference between a rate, a ratio, and a proportion?

EQ: How do I determine if two ratios make a proportion? Vocabulary Lesson 2 Means: Second and third terms Extremes: First and fourth terms. Cross Products: Multiply means and extremes. 12 12 means extremes EQ: How do I determine if two ratios make a proportion?

Use the Pictures to Make some ratios Lesson 2 What is the ratio of: 1. dogs to mice? 2. Mice to flowers? 3. Flowers to dogs? 4. dogs to animals? 5. Mice to living things? Can any of these ratios be reduced? Remember, when you reduce you are finding an equivalent fraction! EQ: How do I determine if two ratios make a proportion?

HOW DO I DETERMINE IF TWO RATIOS MAKE A PROPORTION? 7.4: Rates, Ratios, and Proportions Lesson 2

Two-Column Notes Example 1: Watch Me Lesson 2 Are the ratios 15/30 and 3/6 equivalent? 30 x 3 = 90 15 x 6 = 90 15 6 3 30 = √ Yes, the product of the means is equal to the product of the extremes. So, the ratios are equivalent and form a proportion. means extremes EQ: How do I determine if two ratios make a proportion?

Two-Column Notes Steps to determine if two ratios form a proportion Lesson 2 Step 1: Multiply means Step 2: Multiply extremes Step 3: Compare If products are same, ratios are equivalent and form proportion If not, ratios are not equivalent and do not form proportion EQ: How do I determine if two ratios make a proportion?

Two-Column Notes Example 1: Watch Me Lesson 2 Are the ratios 15/30 and 3/6 equivalent? 30 x 3 = 90 15 x 6 = 90 15 6 3 30 = √ Yes, the product of the means is equal to the product of the extremes. So, the ratios are equivalent and form a proportion. means extremes EQ: How do I determine if two ratios make a proportion?

EQ: How do I determine if two ratios make a proportion? Two-Column Notes Example 2: Help Me Lesson 2 Julie wants to paint her room pink. The ratio to make pink paint is 1 part red to 4 parts white. If Julie has 5 pints of red paint and 15 pints of white paint, will she get the right color pink? Explain. 1 4 15 5 20 No, Julie will not get the right color of pink because 1 to 4 is not the same ratio as 5 to 15. 1 x 15 = 15 but 4 x 5 = 20. = 15 EQ: How do I determine if two ratios make a proportion?

EQ: How do I determine if two ratios make a proportion? Two-Column Notes Example 3: You Try Lesson 2 Is 1:3 the same ratio as 3:9? Use the means and extremes to find your answer. 1 9 3 = 9 Yes! 9 EQ: How do I determine if two ratios make a proportion?

HOW DO I SOLVE A PROPORTION? 7.4: Rates, Ratios, and Proportions Lesson 3

Can you solve this problem? Lesson 3 The ratio of orange juice to pineapple juice in Tropical Treat Punch is 4 to 3. Bill has 64 oz of orange juice. How much pineapple juice does he need? EQ: How do I solve a proportion?

EQ: How do I solve a proportion? Solving Proportions Lesson 3 What does the word proportion mean? What are the three ways to determine if two ratios are equivalent? 1. Reducing 2. Renaming 3. Cross Products EQ: How do I solve a proportion?

EQ: How do I solve a proportion? Example 1 Lesson 3 What is the value of t in the proportion? 20 36 ÷4 5 t = ÷4 = 9 EQ: How do I solve a proportion?

EQ: How do I solve a proportion? Example 2 Lesson 3 The ratio of squirrels to chipmunks in the yard was 2:7. How many squirrels were in the yard if there were 49 chipmunks? 2 7 x7 x 49 = 14 = x7 EQ: How do I solve a proportion?

EQ: How do I solve a proportion? Example 3 Lesson 3 A camp hires 3 counselors for every 25 campers. This year the camp hired 15 counselors. How many campers will be at camp this year? 25 x 15 ÷ 3 375 ÷ 3 125 n = 125 3 25 15 n = EQ: How do I solve a proportion?

EQ: How do I solve a proportion? Coached Example Lesson 3 The ratio of games that Ty’s softball team won to the number of games played is 5 to 9. If the team played 27 games this season, how many games did the team win? 5 x 27 ÷ 9 135 ÷ 9 15 w = 15 5 9 w 27 = EQ: How do I solve a proportion?

EQ: How do I solve a proportion? Solve this problem! Lesson 3 The ratio of orange juice to pineapple juice in Tropical Treat Punch is 4 to 3. Bill has 64 oz of orange juice. How much pineapple juice does he need? EQ: How do I solve a proportion?

HOW DO I SOLVE A RATE? 7.4: Rates, Ratios, and Proportions Lesson 4

Rates A comparison of numbers with different units. Lesson 4 35 miles per 1 hour 99 cents for 1 EQ: How do I solve a rate?

Unit Rate rates out of 1 Lesson 4 When the rate doesn’t give a second number, it is 1. Examples: 120 beats per minute 120 beats in 1 minute $70 per month $70 in 1 month 60 miles per hour 60 miles in 1 hour EQ: How do I solve a rate?

You solve rates just like you solve proportions! Lesson 4 What are the three ways to solve a proportion? Reduce Rename Cross Multiply Sometimes you will have to use cross multiplication! EQ: How do I solve a rate?

Example 1 Watch Me Lesson 4 Kristen scored 126 point in 6 games. She scored the same number of point in each game. How many points did Kristen score per game? ÷6 126 6 p 1 = 21 = ÷6 So, Kristen scored 21 points per game. EQ: How do I solve a rate?

÷3 ÷2 = 45 = 50 ÷3 ÷2 Example 2 Help Me 135 3 m 1 100 2 m 1 = = Lesson 4 Steve took a train and traveled 135 miles in 3 hours. Maria took a bus and traveled 100 miles in 2 hours. Who traveled at a greater rate of speed? ÷3 135 3 m 1 ÷2 = 45 100 2 m 1 = 50 = = ÷3 ÷2 So, Maria traveled at a greater rate of speed because she travels 50 miles per hour. Steve only travels 45 miles per hour. EQ: How do I solve a rate?

Example 3 You Try Lesson 4 It costs $420 to stay 4 nights at the Swan Bay Hotel. What is the price per night? ÷4 420 4 p 1 = 105 = ÷4 So, it costs $105 to stay one night at the Swan Bay Hotel. EQ: How do I solve a rate?

Workout Coach Rates Show Me Complete the given problems. Lesson 4 Complete the given problems. Stay with me and do not go ahead. Show all work! Show Me EQ: How do I solve a rate?

HOW DO I SOLVE A PERCENT PROBLEM? 7.4: Rates, Ratios, and Proportions Lesson 5

Have you ever… Riddle What do these 3 things have in common? Lesson 5 Gone out to eat at a restaurant and left the server a tip? Shopped at a sale like on Black Friday? Taken a test? Riddle What do these 3 things have in common? Percents!!! Where else in real-life (not school) do you deal with percents? EQ: How do I solve a percent problem?

Percent Proportion is % = of 100 Lesson 5 When you hear or see the word percent (%)… Think: “Is over of equals percent over 100.” Write is % = of 100 EQ: How do I solve a percent problem?

EQ: How do I solve a percent problem? Percent Proportion Lesson 5 is of % 100 = Part Total Percent: out of 100 EQ: How do I solve a percent problem?

Watch Me is % 25% x = of 80 100 80 x 25 ÷ 100 2000 ÷ 100 20 X = 20 Think: “Is over of equals percent over 100.” Watch Me Lesson 5 What is 25% of 80? 80 x 25 ÷ 100 2000 ÷ 100 20 X = 20 is % 25% x = of 80 100 EQ: How do I solve a percent problem?

Think: “Is over of equals percent over 100.” Help Me Lesson 5 What percent of 80 is 16? 16 x 100 ÷ 80 1600 ÷ 80 20 % = 20% is % % 16 = of 80 100 EQ: How do I solve a percent problem?

Think: “Is over of equals percent over 100.” You Try Lesson 5 21 is 30% of what? 21 x 100 ÷ 30 2100 ÷ 30 70 x = 70 is % 30 21 = of x 100 EQ: How do I solve a percent problem?