Ratios of Fractions and Their Unit Rates

Video solutions to help Grade 7 students learn how to use ratio tables and ratio reasoning to compute unit rates associated with ratios of fractions.

New York State Common Core Math Grade 7, Module 1, Lesson 11, Lesson 12

Download the Worksheets for Grade 7, Module 1, lesson 11 (pdf)
Download the Worksheets for Grade 7, Module 1, lesson 12 (pdf)

Lesson Outcome

• Students use ratio tables and ratio reasoning to compute unit rates associated with ratios of fractions in the context of measured quantities, e.g., recipes, lengths, areas, and speed. • Students work together and collaboratively to solve a problem while sharing their thinking process, strategies, and solutions with the class. • Students use unit rates to solve problems and analyze unit rates in the context of the problem.

Lesson Summary

• A fraction whose numerator or denominator is itself a fraction is called a complex fraction.

Recall: A unit rate is a rate, which is expressed as A/B units of the first quantity per 1 unit of the second quantity for two quantities A and B.

NYS Math Module 1 Grade 7 Lesson 11

Lesson 11 Example 1: Who is Faster?

During their last workout, Izzy ran 2 ¼ miles in 15 minutes, and her friend Julia ran 3 ¾ miles in 25 minutes. Each girl thought she were the faster runner. Based on their last run, which girl is correct?
Solve using tables, bar models, equations, pictures and double number line.

Exercises

1. A turtle walks 7/8 of a mile in 50 minutes. What is the unit rate expressed in miles per hour?
   a. To find the turtle’s unit rate, Meredith wrote and simplified the following complex fraction. Explain how the fraction 5/6 was obtained.
   b. Did Meredith simplify the complex fraction correctly? Explain how you know.
2. For Anthony’s birthday his mother is making cupcakes for his 12 friends at his daycare. The recipe calls for 3 1/3 cups of flour. This recipe makes 2 1/2 dozen cookies. Anthony’s mother has only 1 cup of flour. Is there enough flour for each of his friends to get a cupcake? Explain and show your work.
3. Sally is making a painting for which she is mixing red paint and blue paint. The table below shows the different mixtures being used.
   a. What are the unit rates for the values?
   b. Is the amount of blue paint proportional to the amount of red paint?
   c. Describe, in words, what the unit rate means in the context of this problem.

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Lesson 11 Example 1: Who is Faster?

During their last workout, Izzy ran 2 ¼ miles in 15 minutes, and her friend Julia ran 3 ¾ miles in 25 minutes. Each girl thought she were the faster runner. Based on their last run, which girl is correct?
Solve using tables, bar models, equations, pictures and double number line.

Lesson 11 Exit Ticket

Which is the better buy? Show your work and explain your reasoning.
3 1/2 lb. of turkey for ten and one-half dollars
2 ½ lb. of turkey for six and one-quarter dollars.

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NYS Math Module 1 Grade 7 Lesson 12

Example 1: Time to Remodel

You have decided to remodel your bathroom and put tile on the floor. The bathroom is in the shape of a rectangle and the floor measures 14 feet 8 inches long, 5 feet 6 inches wide. The tile you want to use costs $5 each, and each tile covers 4 2/3 square feet. If you have $100 to spend, do you have enough money to complete the project?
Make a Plan: Complete the chart to identify the necessary steps in the plan and find a solution.

Exercises

1. Which car can travel further on 1 gallon of gas?
   Blue Car: Travels 18 2/5 miles using 0.8 gallons of gas
   Red Car: Travels 17 2/5 miles using 0.75 gallons of gas

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Lesson 12 Problem Set Sample Solutions

1. You are getting ready for a family vacation. You decide to download as many movies as possible before leaving for he road trip. If each movie takes 1 2/5 hours to download and you downloaded for 5 ¼ hours, how many movies did you download?
   
   
2. The area of a blackboard is 1 1 /3 square yards. A poster’s area is 8/9 square yards. Find a unit rate and explain, in words, what the unit rate means in the context of this problem. Is there more than one unit rate that can be calculated? How do you know?
   
   
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?

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