Lesson 13: Finding Equivalent Ratios Given the Total Quantity

Essential Question: Can we use tables to find an equivalent ratio of two partial quantities given a part-to-part ratio and the total of those quantities?


[expand title=”Warm up”]

Molly runs \frac{1}{3} of a mile in 4 minutes.

  1. If Molly continues at the same speed, how long will it take her to run one mile?
  2. Draw and label a picture showing why your answer to part (a) makes sense.



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When a business buys a fast food franchise, it is buying the recipes used at every restaurant with the same name. For example, all Pizzeria Specialty House Restaurants have different owners but they must all use the same recipes for their pizza, sauce, bread, etc. You are now working at your local Pizzeria Specialty House restaurant and listed below are the amounts of meat used on one meat-lovers pizza.

What is the total amount of toppings used on a meat-lovers pizza? _________________________ cups








The meat must be mixed using this ratio to ensure that customers will receive the same great tasting meat-lovers pizza from every Pizzeria Specialty House Restaurant nationwide. The table below shows 3 different orders for meat-lovers pizza on Superbowl Sunday. Using the amounts and total for one pizza given above, fill in every row and column of the table so the mixture tastes the same.






Pizzeria Specialty House

7.1.13 Ratios with Fractions




S S.52 Example 1 (Group work)

A group of 6 hikers are preparing for a one-week trip. All of the group’s supplies will be carried by the hikers in backpacks. The leader decided that it would be fair for each hiker to carry a backpack that is the same fraction of his weight as all the other hiker’s. In this set-up, the heaviest hiker would carry the heaviest load. The table below shows the weight of each hiker and the weight of his/her backpack.
Complete the table. Find the missing amounts of weight by applying the same ratio as the first 2 rows.



T Example 1 Cont.

  • Based on the given values and found values, is the backpack weight proportional to the hiker’s weight? How do you know?


  • Describe the process of writing and using equations to find the missing values of a quantity (y=xk).




S.53 Example 2



  • What must you calculate or know to complete this table?


  • How many pizzas were made for Order 1? Explain how you obtained and used your answer?


  • Is it possible to order 1 ½ or 2 ½ pizzas? If so, describe the steps to determine the amount of each ingredient necessary.





S.54 Exercise 1 (Partner Work)





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[expand title=”Problems”]

S S.55-57



[expand title=”Exit”]


If 2\frac{1}{2} lb. of candy cost $10, how much would 1 lb. of candy cost?