PERCENTS
Percent means “per hundred.” Writing a number as a percent is a way of comparing the number
*+
with 100. For example: 42% = , --
Percents are really fractions (or ratios) with a denominator of 100. Any percent may be changed to
an equivalent fraction by dropping the percent symbol and writing the number over 100. Usually it is
best to put this fraction in simplest terms.
CHANGING PERCENTS TO DECIMALS
RULE: To change a percent to a decimal, drop the % symbol and move the decimal point two places to
the left.
Examples: 25% = 0.25 75% = 0.75 6.8% = 0.068 0.63% = 0.0063
CHANGING DECIMALS TO PERCENTS
RULE: To change a decimal to a percent, move the decimal point two places to the right and use the
% symbol.
Examples: 0.27= 27% 4.89 = 489% 0.2 = 20% 25 = 2500%
CHANGING PERCENTS TO FRACTIONS
RULE: To change a percent to a fraction, drop the % symbol and write the original number over 100.
Simplify the fraction to lowest terms.
B+ C,
Examples: 62% = =
,-- D-
*.D *.D E ,- *D F
4.5% = = = =
,-- ,-- E ,- ,--- +--
To create a whole number in the numerator, multiply the numerator and denominator by 10. Simplify.
G IJ
, C+ H BD , BD ,C
32 + % = , -- = ,--H = + E , -- = + -- = *-
, ,
Writing 32 + % over 100 produces a complex fraction, so we change 32 + to an improper
fraction and simplify.
CHANGING FRACTIONS TO PERCENTS
RULE: To change a fraction to a percent, change the fraction to a decimal and then change the decimal
to a percent.
Examples:
K
, - = 0.7 = 70%
K
Change , - to a decimalby dividing 7 by 10. Then change the resulting decimal 0.7 to a percent by
moving the decimal point two places to the right and use the % symbol.
C
L = 0.375 = 37.5%
C
Change L to a decimal by dividing 3 by 8. Then change the decimal to a percent by moving the decimal
point tow places to the right and use the % symbol. Division equals 0.375 which becomes 37.5%.
, BASIC PERCENT WORD PROBLEMS
There are three types of word problems associated with percents:
Type A: What number is 15% of 63?
Type B: What percent of 42 is 21?
Type C: 25 is 40% of what number?
The method we use to solve all three types of problems involves translating the sentences
into equations and then solving the equations.
The following translations are used to equations:
English Mathematics
is =
of x (multiply)
a number n
what percent n
what number n
The word is always translates to an = sign, the word of almost always means multiply, and
the number we are looking for can be represented with a letter, such as n or x.
Example 1 (Type A): What number is 15% of 63?
We translate the sentence into an equation as follows:
What number is 15% of 63?
n = 0.15 · 63
To do arithmetic with percents, we have to change percents to decimals.
Solving the equation, we have:
n = 0.15 · 63
n = 9.45
15% of 63 is 9.45
Example 2 (Type B): What percent of 42 is 21?
We translate the sentence into an equation as follows:
What percent of 42 is 21?
n ·42=21
We solve for n by dividing both sides by 42.
Q·*+ = +,
*+ *+
+,
R = *+
R = 0.50
Since the original problem asked for a percent, we change 0.50 to a
percent. R = 0.50 = 50%
21 is 50% of 42
Percent means “per hundred.” Writing a number as a percent is a way of comparing the number
*+
with 100. For example: 42% = , --
Percents are really fractions (or ratios) with a denominator of 100. Any percent may be changed to
an equivalent fraction by dropping the percent symbol and writing the number over 100. Usually it is
best to put this fraction in simplest terms.
CHANGING PERCENTS TO DECIMALS
RULE: To change a percent to a decimal, drop the % symbol and move the decimal point two places to
the left.
Examples: 25% = 0.25 75% = 0.75 6.8% = 0.068 0.63% = 0.0063
CHANGING DECIMALS TO PERCENTS
RULE: To change a decimal to a percent, move the decimal point two places to the right and use the
% symbol.
Examples: 0.27= 27% 4.89 = 489% 0.2 = 20% 25 = 2500%
CHANGING PERCENTS TO FRACTIONS
RULE: To change a percent to a fraction, drop the % symbol and write the original number over 100.
Simplify the fraction to lowest terms.
B+ C,
Examples: 62% = =
,-- D-
*.D *.D E ,- *D F
4.5% = = = =
,-- ,-- E ,- ,--- +--
To create a whole number in the numerator, multiply the numerator and denominator by 10. Simplify.
G IJ
, C+ H BD , BD ,C
32 + % = , -- = ,--H = + E , -- = + -- = *-
, ,
Writing 32 + % over 100 produces a complex fraction, so we change 32 + to an improper
fraction and simplify.
CHANGING FRACTIONS TO PERCENTS
RULE: To change a fraction to a percent, change the fraction to a decimal and then change the decimal
to a percent.
Examples:
K
, - = 0.7 = 70%
K
Change , - to a decimalby dividing 7 by 10. Then change the resulting decimal 0.7 to a percent by
moving the decimal point two places to the right and use the % symbol.
C
L = 0.375 = 37.5%
C
Change L to a decimal by dividing 3 by 8. Then change the decimal to a percent by moving the decimal
point tow places to the right and use the % symbol. Division equals 0.375 which becomes 37.5%.
, BASIC PERCENT WORD PROBLEMS
There are three types of word problems associated with percents:
Type A: What number is 15% of 63?
Type B: What percent of 42 is 21?
Type C: 25 is 40% of what number?
The method we use to solve all three types of problems involves translating the sentences
into equations and then solving the equations.
The following translations are used to equations:
English Mathematics
is =
of x (multiply)
a number n
what percent n
what number n
The word is always translates to an = sign, the word of almost always means multiply, and
the number we are looking for can be represented with a letter, such as n or x.
Example 1 (Type A): What number is 15% of 63?
We translate the sentence into an equation as follows:
What number is 15% of 63?
n = 0.15 · 63
To do arithmetic with percents, we have to change percents to decimals.
Solving the equation, we have:
n = 0.15 · 63
n = 9.45
15% of 63 is 9.45
Example 2 (Type B): What percent of 42 is 21?
We translate the sentence into an equation as follows:
What percent of 42 is 21?
n ·42=21
We solve for n by dividing both sides by 42.
Q·*+ = +,
*+ *+
+,
R = *+
R = 0.50
Since the original problem asked for a percent, we change 0.50 to a
percent. R = 0.50 = 50%
21 is 50% of 42
