Fractions converted to a percent
Problem: Last marking period, Ms. Jones gave an A grade to 15 out of every 100
students and Mr. McNeil gave an A grade to 3 out of every 20 students.
What percent of each teacher's students received an A?
Solution
Teacher
Ratio
Fraction
Percent
Ms. Jones
15 to 100
15%
Mr. McNeil
3 to 20
15%
Solution: Both teachers gave 15% of their students an A last marking period.
In the problem above, the fraction for Ms. Jones was easily converted to a percent. This is
because It is easy to convert a fraction to a percent when the denominator is 100. If a
fraction does not have a denominator of 100, you can convert it to an equivalent
fraction with a denominator of 100, and then write the equivalent fraction as a percent. This
is what was done in the problem above for Mr. McNeil. Let's look at some problems in
which we use equivalent fractions to help us convert a fraction to a percent.
Example 1: Write each fraction as a percent:
Solution
Fraction
Equivalent
Fraction
Percent
50%
90%
80%
Example 2: One team won 19 out of every 20 games played, and a second team won 7 out
of every 8 games played. Which team has a higher percentage of wins?
Solution
Team
Fraction
Equivalent
Fraction
Percent
1
95%
2
87.5%
Solution:
The first team has a higher percentage of wins.
In Examples 1 and 2, we used equivalent fractions to help us convert each fraction to a
percent. Another way to do this is to convert each fraction to a decimal, and then convert
each decimal to a percent. To convert a fraction to a decimal, divide its numerator by
its denominator. Look at Example 3 below to see how this is done.
Example 3: Write each fraction as a percent:
Solution
Fraction
Decimal
Percent
87.5%
95%
1.5%
Now that you are familiar with writing fractions to a percent, do you see a pattern in the problem
below?
Problem: If 165% equals
, and 16.5% equals
, then what fraction is equal to 1.65%?
Solution
Percent
Fraction
165%
16.5%
1.65%
Summary: To write a fraction as a percent, we can convert it to an equivalent fraction with
a denominator of 100. Another way to write a fraction as a percent is to divide
its numerator by its denominator, then convert the resulting decimal to a
percent.
Key words: ratio, fraction, numerator, denominator, decimal, percent, multiplying, dividing,
adding, subtracting, moving the decimal, converting, simplifying, reducing, whole numbers,
operations.