Finding Equivalent Ratios Given the Total Quantity

Examples, videos, and solutions to help Grade 7 students learn how to to find an equivalent ratio of two partial quantities given a part-to-part ratio and the total of those quantities.

New York State Common Core Math Grade 7, Module 1, Lesson 13

Worksheets for Grade 7

Lesson 13 Outcome

• Students use tables to find an equivalent ratio of two partial quantities given a part-to-part ratio and the total of those quantities, in the third column, including problems with ratios of fractions.

Lesson 13 Summary

• To find missing quantities in a ratio table where a total is given, determine the unit rate from the ratio of two given quantities and use it to find the missing quantities in each equivalent ratio.

NYS Math Module 2 Grade 7 Lesson 13 Examples

Example 1
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 of the other hikers’. 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.

Example 2
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.
1/4 cup of sausage
1/3 cup of pepperoni
1/6 cup of bacon
1/8 cup of ham
1/8 cup of beef
What is the total amount of toppings used on a meat-lovers pizza?
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.

Exercise 1

1. The table below shows 6 different-sized pans of the same recipe for macaroni and cheese. If the recipe relating the ratio of ingredients stays the same, how might it be altered to account for the different sized pans?

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