Percent is another way of saying "out of 100," and it is one way of representing a smaller part of a larger whole. One way to picture this is to use a percent bar. This is a bar that is marked with percent on one side and the actual part and whole on the other.
The images to the left and right represent the same part of the whole. However, the image on the left shows fewer division marks than the image on the right. From these two images, you can determine more precisely from the image on the right that the green part covers about 38% of the whole bar. The more equally divided marks you can show on your percent bar, the more acurate you will be with your answer.
In the following activity, you will practice using a percent bar to find the value of a percent, given values for the part and the whole.
Drag each green bar onto the empty percent bar, and then click the appropriate place on the percent scale on the right side of the bar.
Copy the following table into your notes. Use the results from the interactive to fill in the missing information.
| Part | Whole | Percent | Percent ÷ 100 |
| 2 | 40 | ||
| 4 | 40 | ||
| 5 | 40 | ||
| 8 | 40 | ||
| 10 | 40 | ||
| 20 | 40 | ||
| 30 | 40 | ||
| 40 | 40 |
| Part | Whole | Percent | Percent ÷ 100 |
| 2 | 40 | 5% | 0.05 |
| 4 | 40 | 10% | 0.1 |
| 5 | 40 | 12.5% | 0.125 |
| 8 | 40 | 20% | .2 |
| 10 | 40 | 25% | .25 |
| 20 | 40 | 50% | .5 |
| 30 | 40 | 75% | .75 |
| 40 | 40 | 100% | 1.0 |
Answer the following questions based on the information found in the first three columns of the table.
What relationship do you notice between the sizes of the parts compared to the size of the percent? (with the same whole)
Interactive popup. Assistance may be required. The larger the part, the larger the percent.
Based on the information in the table, what is 10% of 40?
Interactive popup. Assistance may be required. 4 is 10% of 40
Based on the information in the table, what is 20% of 40?
Interactive popup. Assistance may be required. 8 is 20% of 40
What scale factor do you use to move from 10% to 20%?
Interactive popup. Assistance may be required. A scale factor of 2
What scale factor do you use to move from 4 to 8?
Interactive popup. Assistance may be required. A scale factor of 2
What does this tell you about using a percent bar to estimate percent?
Interactive popup. Assistance may be required. If you use a percent bar to find one percent, you can use a scale factor to find another percent
What scale factor do you use to move from 10% to 50%?
Interactive popup. Assistance may be required. A scale factor of 5
If you use this same scale factor on 4, what is the result?
Interactive popup. Assistance may be required. 5(4) = 20
What does this result tell you?
Interactive popup. Assistance may be required. 50% of 40 is 20
From the information in the table, what is 50% of 40?
Interactive popup. Assistance may be required. 50% of 40 is 20
To answer the following questions refer back to the information in the completed table.
| Part | Whole | Percent | Percent ÷ 100 |
| 2 | 40 | 5% | 0.05 |
| 4 | 40 | 10% | 0.1 |
| 5 | 40 | 12.5% | 0.125 |
| 8 | 40 | 20% | .2 |
| 10 | 40 | 25% | .25 |
| 20 | 40 | 50% | .5 |
| 30 | 40 | 75% | .75 |
| 40 | 40 | 100% | 1.0 |
What is the relationship between the part, the whole, and the percent ÷ 100?
Interactive popup. Assistance may be required. Part ÷ whole = percent ÷ 100
How could you rewrite this relationship as a proportion:
Interactive popup. Assistance may be required.
Part over Whole
Part
Whole
=
Percent over 100
Percent
100
From this, you can calculate a percent by dividing the part by the whole to get a decimal, and then multiply by 100.
Example: There are 75 students in the middle school orchestra. 60 of those students play instruments with strings. What percent of the orchestra play an instrument with strings?
Click on the name of each method to see the solution.
10% of 75 is 7.5, which means that 20% of 75 is 15.
Use the information above to answer the following questions:
What scale factor do you need to use to convert from 15 to 60?
Interactive popup. Assistance may be required. A scale factor of 4
Use this information to convert from 20% to the unknown percent that you want to find.
Interactive popup. Assistance may be required. 4(20%) = 80%
Drag the green bar onto the empty percent bar and then click to see the answer:
Now try this one. Sketch your own percent bar or use a calculator.
Travis is buying a pair of running shoes at a clearance sale. The shoes originally cost $36.00, and Travis saved a total of $9.00 because of the sale. What percent of the original cost did Travis save?
Interactive popup. Assistance may be required.
Calculator
9 ÷ 36 = decimal
decimal(100) = percent
Interactive popup. Assistance may be required.
Calculator
9 ÷ 36 = 0.25
.25(100) = 25
9 is 25% of 36.