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

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:

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.

*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.