Lesson 11
Representing Ratios with Tables
Let’s use tables to represent equivalent ratios.
11.1: How Is It Growing?
Look for a pattern in the figures.
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How many total tiles will be in:
- the 4th figure?
- the 5th figure?
- the 10th figure?
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How do you see it growing?
![A growing pattern of tiles arranged in rows.](https://staging-cms-im.s3.amazonaws.com/rdZLvFPmkmYMhg2ry36wjCxP?response-content-disposition=inline%3B%20filename%3D%226-6.2.D1_Image_1.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.D1_Image_1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T092953Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6783b28c46cf87a3ebe7f9a058fef9a169b7c70ee4a8e4494b2de9ad5d60e593)
11.2: A Huge Amount of Sparkling Orange Juice
Noah’s recipe for one batch of sparkling orange juice uses 4 liters of orange juice and 5 liters of soda water.
- Use the double number line to show how many liters of each ingredient to use for different-sized batches of sparkling orange juice.
- If someone mixes 36 liters of orange juice and 45 liters of soda water, how many batches would they make?
- If someone uses 400 liters of orange juice, how much soda water would they need?
- If someone uses 455 liters of soda water, how much orange juice would they need?
- Explain the trouble with using a double number line diagram to answer the last two questions.
11.3: Batches of Trail Mix
A recipe for trail mix says: “Mix 7 ounces of almonds with 5 ounces of raisins.” Here is a table that has been started to show how many ounces of almonds and raisins would be in different-sized batches of this trail mix.
almonds (oz) | raisins (oz) |
---|---|
7 | 5 |
28 | |
10 | |
3.5 | |
250 | |
56 |
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Complete the table so that ratios represented by each row are equivalent.
- What methods did you use to fill in the table?
- How do you know that each row shows a ratio that is equivalent
to \(7:5\)? Explain your reasoning.
You have created a best-selling recipe for chocolate chip cookies. The ratio of sugar to flour is \(2:5\).
Create a table in which each entry represents amounts of sugar and flour that might be used at the same time in your recipe.
- One entry should have amounts where you have fewer than 25 cups of flour.
- One entry should have amounts where you have between 20–30 cups of sugar.
- One entry can have any amounts using more than 500 units of flour.
Summary
A table is a way to organize information. Each horizontal set of entries is called a row, and each vertical set of entries is called a column. (The table shown has 2 columns and 5 rows.) A table can be used to represent a collection of equivalent ratios.
Here is a double number line diagram and a table that both represent the situation: “The price is \$2 for every 3 mangos.”
![A double number line with 6 evenly spaced tick marks: For "price in dollars" the numbers 0, 2, 4, 6, 8, and 10 are indicated. For "number of mangos" the numbers 0, 3, 6, 9, 12, and 15 are indicated.](https://staging-cms-im.s3.amazonaws.com/wzfPLctnTSRzi97K5DuFhQpV?response-content-disposition=inline%3B%20filename%3D%226-6.2.D1_Image_6.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.D1_Image_6.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T092953Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=09557a506196ccb748f8226468ae6855751566115f93b7c3848903944550f066)
![2-column table, 5 rows of data. First column labeled "price in dollars,” second column labeled "number of mangos." The data is as follows: Row 1: 2, 3 Row 2: 4, 6 Row 3: 6, 9 Row 4: 8, 12 Row 5: 10, 15.](https://staging-cms-im.s3.amazonaws.com/oQ6AF3VwxLzQdn1j3JW7M41b?response-content-disposition=inline%3B%20filename%3D%226-6.2.D1_Image_7.1.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.D1_Image_7.1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T092953Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f9e31a17f11e53dcd4f730fe09e9ddb79c844eaba858d80ea4fc9f136047ca54)
Glossary Entries
- table
A table organizes information into horizontal rows and vertical columns. The first row or column usually tells what the numbers represent.
For example, here is a table showing the tail lengths of three different pets. This table has four rows and two columns.
pet tail length (inches) dog 22 cat 12 mouse 2