Introduction
Math problems involving
percentages are often
presented as “word”
problems. Percentages can
help make data more
digestible. For example,
instead of saying that five
out of every eight students
passed the math test
yesterday, you can report
that only 62.5 percent of
the students passed the
test. Students might be able
to understand the percentage
better. In the M.A.R.S.
mission working data into
percentages also allows
students to make critical
decisions about their
mission.
Learning to calculate
percentages is not difficult. Knowing just a few
key terms allows students to easily translate a
percentage word problem into a mathematical
expression they can solve.
Duration
30 minutes
Materials
Procedure

Read and review the
information on the worksheet in class.

Check for understanding
throughout the review.

Do the problem examples
on the board, if necessary, to reinforce the
steps for translating the words into
mathematical terms.

Have the students
complete the problems and check for
understanding.
How to Translate Percentage
Word Problems
“Percent” comes from Latin
and means "for every hundred.” So, when you hear
that “50 percent of the students passed the math
test,” it means that for every 100 students,
only 50 passed the test.
“Of” means “multiplied by.”
For example:
What is 50 percent of 20?
What is 50 percent X 20?
Answer = 10.
“Is” always means “equals.
“Per” means “divided by.”
For example:
If you drive 300 miles and
you were driving 60 miles per hour, how many
hours does your trip take?
300 divided by 60 = 5 hours
“%” means “per one hundred.”
To get a decimal that you can use in a
multiplication or division problem, divide by
100. For example:
50% means
50
divided by 100, or 0.50
“What” can be replaced by
what number you are trying to find. You can
usually replace this with “X” to solve the
equation you now have in mathematical terms.
The key terms listed above
have been summarized in this table. As you
review the following examples and work the
practice problems, refer to this table to
translate the following problems into
mathematical expressions you can solve.
Term 
Mathematical Expression 
percent 
"for every one
hundred" 
of 
"Multiplied by" or "times" 
is 
"equals" 
per 
"divided by" 
% 
"percent" 
what 
(the number you are trying to find
can be replaced with "x") 
Examples:

What is 50 percent of 30?
Translation: X
= .50 × 30
X = 15

11 is what percent of 44?
Translation: 11 = (X/100)
×
44?
X = 25
%
Solve these problems:

What is 35 percent
of 80?

16 percent of what
number is 2?

43 percent of what
number is 34?

Amanda loves blue
clothes. She has more blue outfits than any
other color of clothes! Her best friend notices
that Amanda wears blue for 68 percent of school
days. In a school year of 180 days, how many
days does Amanda wear Blue?

When one of your teachers
was 15, he weighed 92 percent of his weight
today. Back then he weighed 115 lbs. How much
does he weigh today?

Michael had a sore
throat, and his doctor estimated that he had
156,000 strep bacteria in his throat. By the
time he got this medicine, he had 250 percent
more bacteria! How many bacteria did he have
now?
Answer Key
Solve these problems:

What is 35 percent
of 80?
x =
(35%) (80)
x =
(.35) (80)
x =
28

16 percent of what
number is 2?
(16) (X) = 2
X = 12.5

43 percent of what
number is 34?
(43%) (X) = 32
(.43) (X) = 32
X = 74

Amanda loves blue
clothes. She has more blue outfits than any
other color of clothes! Her best friend notices
that Amanda wears blue for 68 percent of school
days. In a school year of 180 days, how many
days does Amanda wear blue?
(68%) (180) = days
(.68) (180) = 122.4 days

When one of your teachers
was 15, she weighed 92% of his weight today.
Back then she weighed 115 lbs. How much does she
weigh today?
(92%) (x) = 115
(.92) (x) =
115
x = 115/.92
x = 125 lbs.

Michael had a sore
throat, and his doctor estimated that he had
156,000 strep bacteria in his throat. By the
time he got this medicine, he had 250 percent
more bacteria! How many bacteria did he have
now?
Note: 250
divided by 100 = 2.5
(2.5) (156,000) + (156,000) = x
390,000 + 156,000 = x
546,000
bacteria= x
