Percents

The word percent means “hundredths” or a number which is divided by 100. Converting a number into a percentage involves multiplying the number by 100.

A percent can be determined by performing the division of the part by the total and multiplying it by 100:

Percent = Part x 100

Total

For example, if Wendy missed 12 out of 80 examination questions, what is the percent of questions she missed?

Percent = missed questions x 100 = 12/80 x 100 = 0.15 x 100 = 15%

Total

The phrase “X is N percent of Y” can also be written mathematically as

X = N x Y

100

The word “is” means equal (=), while the word “of” means “multiply”. However, before multiplying, you must change a percent into a decimal or fractional format.

For example:

5 is 20% of 25, means 5 = 0.20 x 25 26

To change the fraction into the percent, you must first change the fraction into a decimal, and then multiply by 100 (or move the decimal point by 2 places to the right)

For example:

Change the fraction 1/5 into a percent.

First, change the fraction 1/5 into the decimal 0.2, and multiply by 100 (move the decimal 2 places to the right). Therefore:

1/5 x 100 = 20%

The following table provides the common percentages that you will use on a regular basis, and may wish to memorize.

Fraction

Decimal

Percent

1/100

0.01

1%

1/10

0.1

10%

1/7

0.1428571

14.3%

1/6

0.16666...

16.6% or 16.7%

1/5

0.2

20%

1/4

0.25

25%

1/3

0.33

33.3%

1/2

0.5

50%

3/5

0.6

60%

1

1.0

100% 27

3/2

1.5

150%

Please note that numbers over 1 achieve percentages that are greater than 100%

Consider the following example:

What is 20% of 50?

A. 5

B. 8

C. 10

D. 12

E. 15

Note: the answer is C

To solve this question, you must rewrite it as an algebraic question. Therefore, let x represent the unknown number.

X = 0.20 x 50

Keep in mind that to change the percent to a decimal, and that the word “of” means that you should multiply.

X = 10

28

Here is another example:

5 is what percent of 2?

A. 2.5%

B. 25%

C. 100%

D. 250%

E. 500%

Rewrite this as an algebraic equation. 5 = n × 2

Solve for n and remember to change the answer to a percent.

n = 5/2 = 2.5 = 250%

Therefore, the answer is (D)