Quantities are often expressed as percents. A percent is a ratio that compares a number to 100. Percent also means per hundred or hundredths. For example, a 5% glucose solution contains 5 grams of glucose in 100 milliliters of solution.
You can express a fraction or a ratio as a percent by using a
proportion in which one denominator is 100.
Example
Express each fraction or ratio as a percent.
1. ⅖ of the circle is shaded.
Alternative
Solutions :
r is the percent.
2(100)
= 5r Find
the cross products.
200 =
5r Multiply
2 and 10
Divide each
side by 5.
40 = r Simplify
2. A study found that 3 out of 8 people switch channels when a commercial is
on television. Source: American Demographics
Alternative
Solutions :
Write a
proportion.
3(100)
= 8r Find
the cross products.
300 = 8r Multiply
3 and 100
Divide each
side by 8.
37.5 =
r 37.5%
of people switch channels.
In Example 1, the number of parts shaded, 2, is called the percentage (P). It
is being compared to the total number of parts, 5, which is called the base (B).
This is an example of a percent proportion.
Example
3. Forty is what percent of 160?
Alternative
Solutions :
Use the percent proportion.
Write “what percent” as 
.
Replace P with 40 and B with 160.
40(100)
= 160r Find the
cross products.
4000 =
160r Multiply
40 and 100
Divide
each side by 8.
25 = r
Simplify.
So, 40 is
25% of 160.
4. 50% of what number is 42.5?
Alternative
Solutions :
Use
the percent proportion.
Write “what percent” as
.
Replace
P with 42.5 and r with 50.
42.5(100)
= 50B Find
the cross products.
4250 =
50B Multiply
425 and 100.
Divide
each side by 50.
85 = B Simplify.
So, 50% of
85 is 42.5.
Businesses can use a time study to determine what percent of
an employee’s time is spent on various activities.
Example
Business Link
5. The manager of The Furniture Store conducted a time study of the
employees in its warehouse. The chart at the right shows the average number of
hours spent on each activity during the workday. What percent of the time do
the employees spend on each activity?
The
employees work 3 + 4 + 1 or 8 hours each day. This is the base. To find each
percent, write and solve the percent proportion for each activity.
The
results are summarized in the chart.
Note
that the total of the percent column is 100%.
Data are often displayed using circle graphs. A circle graph is a graph that
shows the relationship between parts of the data and the whole.
Example
Statistics Link
6. Make a circle graph of the data in
Example 5.
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furniture accounts for 37.5% of the time. A circle is composed of 360°. To find
the number of degrees for this section of the graph, find 37.5% of 360. Repeat
this process for the other sections. Replace B with 360 and r with each
percent.
Use a
compass to draw a circle.
Then
draw a radius. Use a protractor to draw a 135° angle.
You
can start with any of the angles.
From
the new radius, draw a 180° angle. The remaining section should be 45°. Label each
section of the graph with the category and percent. Give the graph a title.
Sumber
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