Solve problems using percent proportion.
After completing this tutorial, you will be able to complete the following:
A proportion is a statement of equality between two ratios.
In this Activity Object, students will solve problems forming proportions. One of the ratios in these problems will be a percent. For example, if we wanted to determine the amount of wood needed to finish building a house, we could create proportion using the information below:
Let's say that the amount of wood needed to finish the house is the part, represented by a, and the total amount of wood is the base, represented by b.If the percent is represented p, we can rewrite the question into the following equation:
Using percent proportion to calculate the percent of a number.
Using the example from above, let's plug in some numbers for this problem. Let b equal 15 tons of wood. Let a equal 9 tons of wood. Now, let's solve the equation for p, the percent of the house completed.
In order to solve this equation, we need to apply the Cross Product Property. This property states that "in a proportion, the product of the means is equal to the product of the extremes."
In the proportion , b and c are the means and a and d are the extremes.
So, the cross product is: ad = bc.
In our problem, the cross product is 15p = 900. 60% of the house is finished.
Using percent proportion to calculate the part of a number given the percent and the base.
We can use the Cross Product Property to determine the part of the number when given the percent and number, or base. Let's use the same example problem from above. This time, we want to find the amount of wood that is needed to finish the house. If we know that the total amount of wood needed is 15 tons and 60% of the house is finished so far, we need to find the part not completed.
Nine tons of wood have been used in the completed house. 15 - 9 = 6, so we need 6 more tons of wood to complete the house.
Other methods can be used to calculate the part.
1. The percent can be converted into a decimal and then multiplied with the whole.
2. The percent can be converted to a fraction and then multiplied with the whole.
|Approximate Time||10 Minutes|
|Pre-requisite Concepts||cross products, operations on whole numbers, percents, proportions|
|Type of Tutorial||Skills Application|
|Key Vocabulary||percent proportion, part, base|