### Per Cents

#### Background

This article assumes that you know what the words in this list mean and understand the mathematics that goes with these words.

• fraction
• numerator
• denominator
• equals
• times
• multiply
• divide
• decimal point

#### Definition

Per cents are simply fractions where the denominator is always 100. (If you don't already know about fractions, this information is not intended for you.) For example, 2 per cent or 2% simply the means the fraction (2/100). If you memorize this definition, you should be able to do any type of per cent problem.

Per cents are fractions where the denominator is 100.
1% = (1/100)
33% = (33/100)

Remember that it doesn't make any difference whether you write a fraction with a slanted division line between the numerator and denominator or with a horizontal division line between the numerator and denominator: #### Practice Problem

What is 30 per cent of 10?

Don't forget that in word problems, is almost always means equals and of almost always means times.

What is 30 per cent of 10?

What equals 30 per cent times 10?

You can use mathematical symbols instead of words. Use = for "equals," % for "per cent," and × for "times."

What = 30% × 10?

You can finish writing this question in standard mathematical format by using the letter W to stand for "what" and omitting the question mark.

W = 30% × 10

Now remembering the definition that % means a fraction with 100 in the denominator, you can rewrite this as follows.

W = (30/100)×10

Now you need to recall from your study of fractions that one way to multiply a fraction by a number is to first multiply the numerator of the fraction by the number and then divide that answer by the denominator.

Step 1.First multiply 30 by 10:
30×10 = 300

Step 2.Next divide 300 by 100:
300/100 = 3

You can probably divide 300 by 100 in your head. But it is useful to remember that an easy way to divide a number by 100 is to move the number's decimal point two places to the left. You should also remember that when a number isn't written with a decimal point, you put the decimal point just to the right of the number.

300 = 300.

300/100 = 300./100 = 3.00

Another rule to remember about decimal points is that if a number has at least one digit before a decimal point and all of the digits after the decimal point are zeros, it doesn't change the numerical value if you omit the zeroes and the decimal point.

#### Summary

Question What is 30 per cent of 10?

Answer 3 is 30 per cent of 10.

W = (30/100)×10
W = ((30×10)/100)
W = 300/100 = 300./100 = 3.00 = 3

• First posted 9/3/2007.
• Revision posted 9/3/2007.