Name _________________________
Date _____________ Period _____
P ROBLEM 4.3 – F INDING A G ENERAL S TRATEGY
Expressing Data in Percent Form
One of the powerful things about mathematics is that you can often find
ways to solve one problem that can also be used to solve similar
problems.
For example, it is easy to find percents when exactly 100 people are
surveyed, since percent means “out of 100.” However, surveys often
involve more than or fewer than 100 people. Here is an example.
A survey asked cat owners, “Does your cat have bad breath?” Out of the
200 cat owners surveyed, 80 answered yes to this question. What percent
of the cat owners answered yes?
As you work on these questions, try to find a way to describe strategies
you can use for solving these kinds of problems.
A.
Suppose 80 out of 400 cat owners surveyed said their cats have bad
breath. What percent of the cat owners is this?
Is this percent greater than, equal to, or less than the percent
represented by 80 out of 200 cat owners? Explain.
B.
If 120 out of 300 seventh-graders surveyed said mathematics is
their favorite subject, how would you express this as a fraction?
Write this fraction as a decimal and as a percent.
C.
Suppose 30 out of 50 adults surveyed said they enjoy their jobs. How
would you express this as a fraction, as a decimal, and as a
percent?
D.
Suppose 34 out of 125 sixth-graders surveyed said they would like to
try hang gliding. What fraction, decimal, and percent is this?
E.
Five out of 73 middle-school students said they look forward to
practicing fire drills. What fraction, decimal, and percent is this?
F.
1. Write an explanation for the different strategies you used to
express the survey data in percent form.
2. What general process will cover all of the cases?
Problem 4.3
Applications
For Exercises 1–9, use the cat data in the table.
1.
a. What fraction of the cats are female?
b. What fraction of the cats are male?
c. Write each fraction as a decimal and as a percent.
2.
a. What fraction of the cats are kittens?
b. What fraction of the cats are adults?
c. Write each fraction as a decimal and a percent.
4.
a. What fraction of the kittens are male?
b. Write the fraction as a decimal and as a percent.
5. What percent of the cats weigh from 11 to 15.9 pounds?
6. What percent of the cats weigh from 0 to 5.9 pounds?
7. What percent of the cats are male kittens and weigh from 11 to 15.9
pounds?
8. What percent of the cats are female and weigh from 6 to 15.9 pounds?
9. What percent of the cats are kittens and weigh from 16 to 20 pounds?
10. What percent of the females weigh from 0 to 5.9 pounds?
For Exercises 11–14 use the following information:
In a recent survey, 150 dog owners and 200 cat owners were asked what
type of food their pets liked. Here are the results of the survey.
11. Find the food category that the greatest number of dog owners say is
favored by their pets. Write the number in this category as a fraction,
as a decimal, and as a percent of the total dog owners surveyed.
12. Find the food category that the greatest number of cat owners say is
favored by their pets. Write the number in this category as a fraction,
as a decimal, and as a percent of the total cat owners surveyed.
13. Suppose only 100 dog owners were surveyed, with similar results.
Estimate how many would have answered in each of the three
categories.
14. Suppose 50 cat owners were surveyed, with similar results. Estimate
how many would have answered in each of the three categories.
15. Elisa’s math test score, with extra credit included, was
percent is this?
16. Suppose 12% of students surveyed said they have tried
rock climbing. Estimate how many would say they
have tried rock climbing if
.What
a. 100 students were surveyed
b. 200 students were surveyed
c. 150 students were surveyed