Unit 7-1 Lessons 11-16 Ratios and Proportional Relationships: Lessons 11-16 Name Date Classwork Book Math 7: Mr. Sanford Lesson 11-16: Proportional Relationships
Lesson 1-11 Lesson 11: Ratios of Fractions and Their Unit Rates Example 1: Who is Faster? During their last workout, Izzy ran 2 ¼ miles in 1 5 hour and her friend Julia ran 3 ¾ miles in hour. Each girl thought she were the 4 12 faster runner. Based on their last run, which girl is correct? Example 2: Turtle, Turtle A turtle walks ⅞ of a mile in 50 minutes. Find the turtle s unit rate in miles per hour using both methods. Grade 7 Lesson 1-11: Ratios of Fractions and Their Unit Rates 3
Lesson 1-11 Exercise Sally is making a painting for which she is mixing red paint and blue paint. The table below shows the different mixtures being used. Red Paint (Quarts) Blue Paint (Quarts) Unit Rates 1 1 2 2 2 5 2 1 2 4 3 3 4 6 1 4 4 6 2 3 1.2 2 1.8 3 a. Is the amount of blue paint proportional to the amount of red paint? b. Describe, in words, what the unit rate means in the context of this problem. Grade 7 Lesson 1-11: Ratios of Fractions and Their Unit Rates 4
Lesson 1-12 Lesson 12: Ratios of Fractions and Their Unit Rates Exercises 1. Which car can travel further on 1 gallon of gas? Blue Car: Travels 18 2 miles using 0.8 gallons of gas 5 Red Car: Travels 17 2 miles using 0.75 gallons of gas 5 2. You are getting ready for a family vacation. You decide to download as many movies as possible before leaving for the road trip. If each movie takes 1 2 hours to download and you downloaded for 5 ¼ hours, how many movies did you download? 5 3. A toy remote control jeep is 12 ½ inches wide while an actual jeep is pictured to be 18 ¾ feet wide. What is the value of the ratio of the width of the remote control jeep to width of the actual jeep? Grade 7 Lesson 1-12: Ratios of Fractions and Their Unit Rates 5
Lesson 1-12 4. 1 3 cup of flour is used to make 5 dinner rolls. a. How much flour is needed to make one dinner roll? b. How many rolls can you make with 5 2 cups of flour? 3 c. How many cups of flour are needed to make 3 dozen dinner rolls? Grade 7 Lesson 1-12: Ratios of Fractions and Their Unit Rates 6
Lesson 1-13 Lesson 13: Finding Equivalent Ratios Given the Total Quantity Example 1: Pizza, Pizza Students in 6 classes, displayed below, ate the same ratio of cheese pizza slices to pepperoni pizza slices. Complete the following table, which represents the number of slices of pizza students in each class ate. Slices of Cheese Pizza Slices of Pepperoni Pizza Total Pizza 7 6 15 8 13 3 4 3 1 3 2 1 10 Grade 7 Lesson 1-13: Finding Equivalent Ratios Given the Total Quantity 7
Lesson 1-13 Example 2: Painting 5. To make green paint, students mixed yellow paint with blue paint. The table below shows how many yellow and blue drops from a dropper several students used to make the same shade of green paint. Complete the table. Yellow (Y) (ml) 3 ½ 5 ¼ Blue (B) (ml) Total 5 6 ¾ 6 ½ Grade 7 Lesson 1-13: Finding Equivalent Ratios Given the Total Quantity 8
Lesson 1-14 Lesson 14: Equations of Fraction Proportional Relationships Example 1: Mother s 10K Race Sam s mother has entered a 10 K race. Sam and his family want to show their support of their mother but they need to figure out where they should go along the race course. They also need to determine how long it will take her to run the race so that they will know when to meet her at the finish line. Previously, his mother ran a 5K race with a time of 1 ½ hours. Assume Sam s mother ran the same rate as the previous race in order to complete the chart. Create a chart that will show how far Sam s mother has run after each half hour from the start of the race and graph it on the grid at the right. Hours (H) Km run (D) a. How far does she run in 1 hour? What is another name for this value? b. Write an equation to model this data. c. How many km would she run in 2 hours? How long would it take her to run 10 km? Grade 7 Lesson 1-14: Equations of Fraction Proportional Relationships 9
Lesson 1-14 Example 2: Organic Cooking After taking a cooking class, you decide to try out your new cooking skills by preparing a meal for your family. You have chosen a recipe that uses an organic mushroom mix as the main ingredient. Using the graph below, complete the table of values and answer the following questions. Weight in Pounds Cost 0 0 ½ 4 1 1 ½ 12 16 2 ¼ 18 1. Is this relationship proportional? How do you know from examining the graph? 2. What is the unit rate for cost per pound? 3. Write an equation to model this data. 4. What ordered pair represents the unit rate and what does it mean? 5. What does the ordered pair (2, 16) mean in the context of this problem? 6. If you could spend $10.00 on mushrooms, how many pounds could you buy? Grade 7 Lesson 1-14: Equations of Fraction Proportional Relationships 10
Lesson 1-15 Lesson 15: Multistep Ratio Problems Example 1: Bargains A retail clothing store advertises the following sale: Shirts are 1 off the original price; pants are 1 off the original price, and shoes are 2 3 1 off the original price (called the discount rate). 4 a. If a pair of shoes cost $40 and is advertised at 1 off the original price, what is the sales price? 4 b. At Peter s Pants Palace a pair of pants that usually sell for $33.00. If Peter advertises that the store is having 1 off sale, 3 what is the sale price of Peter s pants? Example 2: Big Al s Used Cars A used car sales person receives a commission of 1 of the sales price of the car on each car he sells. What would the sales commission be on a car that sold for $24,000? 12 Grade 7 Lesson 1-15: Multistep Ratio Problems 11
Lesson 1-15 Example 3: Deal or No Deal How much will the final cost of a couch be that is marked-up by 1 and then sold at a 1 off discount if the original price is $2400? 3 5 Example 4: Born to Ride A motorcycle dealer paid a $12,000 for a motorcycle and marked it up by 1 5 of the price he paid. What was the price that he sold the motorcycle for? How much was the motorcycle marked up by? Grade 7 Lesson 1-15: Multistep Ratio Problems 12
Lesson 1-16 Lesson 16: Multistep Ratio Problems Example 1: Bargains A retail clothing store advertises the following sale: Shirts are 1 off the original price; pants are 1 off the original price, and shoes are 2 3 1 off the original price (called the discount rate). 4 a. If a pair of shoes is on sale for $40, what was the original price? b. During the sale, a pair of pants sells for $22.00. What was the original price of the pants? Example 2: Big Al s Used Cars A used car sales person receives a commission of 1 of the sales price of the car on each car he sells. What was the cost of the car if he received $1,800? 12 Grade 7 Lesson 1-16: Multistep Ratio Problems 13
Lesson 1-16 Example 3: Tax Time A furniture store sells a couch and gets $500 in profit. If the profits at this store are generally 1 of the original cost, find the original 4 cost before the markup. Example 4: Born to Ride A motorcycle dealer paid a certain price for a motorcycle and marked it up by 1 of the price he paid. Later he sold it for $14,000 5 what is the original price? Grade 7 Lesson 1-16: Multistep Ratio Problems 14