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.
• 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.
• 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.
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.
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.
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?
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.
Exercises1. Which car can travel further on 1 gallon of gas?
Lesson 12 Problem Set Sample Solutions1. 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?
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
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