Proportional Tables Worksheet
Proportional tables are a fundamental concept in mathematics, particularly in algebra and geometry. They are used to represent the relationship between two quantities that are proportional to each other. In this worksheet, we will explore the concept of proportional tables, how to create them, and how to use them to solve problems.
What are Proportional Tables?
Proportional tables are tables that show the relationship between two quantities that are directly proportional to each other. In a proportional table, the ratio of the corresponding values in each row is constant. This constant ratio is called the scale factor.
How to Create a Proportional Table
To create a proportional table, you need to know the scale factor between the two quantities. Here are the steps to create a proportional table:
- Write the two quantities in a table format, with one quantity in each column.
- Choose a value for one of the quantities and write it in the table.
- Multiply the chosen value by the scale factor to get the corresponding value for the other quantity.
- Write the corresponding value in the table.
- Repeat steps 2-4 for several values of the first quantity.
For example, let’s say we want to create a proportional table for the cost of apples, where the cost is directly proportional to the number of apples. If the cost of 2 apples is 3, the scale factor is 1.50 per apple.
| Number of Apples | Cost |
|---|---|
| 2 | $3 |
| 4 | $6 |
| 6 | $9 |
| 8 | $12 |
How to Use Proportional Tables
Proportional tables can be used to solve problems involving proportional relationships. Here are some ways to use proportional tables:
- To find the corresponding value of one quantity given the value of the other quantity, simply look up the value in the table.
- To find the scale factor, divide the corresponding values of the two quantities.
- To create a graph of the proportional relationship, plot the points from the table on a coordinate plane.
For example, let’s say we want to find the cost of 5 apples using the proportional table above. Since the table only goes up to 4 apples, we can use the scale factor to find the cost of 5 apples.
Scale factor = 1.50 per apple Number of apples = 5 Cost = Number of apples x Scale factor = 5 x 1.50 = $7.50
Therefore, the cost of 5 apples is $7.50.
📝 Note: Proportional tables can only be used when the relationship between the two quantities is directly proportional.
Example Problems
Here are some example problems that involve using proportional tables:
- If the cost of 3 books is $15, find the cost of 5 books using a proportional table.
- If the distance traveled by a car in 2 hours is 120 miles, find the distance traveled in 5 hours using a proportional table.
- If the weight of 4 bags of flour is 12 pounds, find the weight of 6 bags of flour using a proportional table.
Try to solve these problems on your own using proportional tables. You can check your answers below.
What is a proportional table?
+A proportional table is a table that shows the relationship between two quantities that are directly proportional to each other.
How do I create a proportional table?
+To create a proportional table, write the two quantities in a table format, choose a value for one of the quantities, and multiply it by the scale factor to get the corresponding value for the other quantity.
How do I use a proportional table to solve problems?
+Proportional tables can be used to find the corresponding value of one quantity given the value of the other quantity, find the scale factor, and create a graph of the proportional relationship.
By understanding how to create and use proportional tables, you can solve a wide range of problems involving proportional relationships. Remember to always check your work and use the scale factor to ensure accuracy.
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