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This page gives you some general advice that will help you translate word problems that involve percents into algebraic expressions.

The word "of" almost always means "multiplied by". Example: What is half of 20? Answer: one-half multiplied by 20, which is 10.

The word "per" almost always means "divided by". Example: I drove 300 miles in 5 hours. I went 60 miles per hour, because the number of miles divided by the number of hours is 60.

The symbol % means percent, which literally means "per hundred". I've already mentioned that "per" usually means divided by, and this is no exception. Percent means "divided by 100". Example: 60% means "60 divided by 100", or 3/5, or 0.6.

The word "what" or "what number" is a placeholder for a number. You can sometimes replace it with "x" to make an algebraic equation. Example: what multiplied by 3 equals 6. This means (x)(3)=6. Now you can solve for x by dividing both sides of the equation by 3. That gives you x=2.

Now, let's put these together. I will use the words "what", "of" and "percent" in a single sentence, then translate them for you.

Example: What is 50% of 30?

Translation: x = (50/100)(30)?

Simplification: x=15, which means 15 is 50% of 30.

Here's another one.

11 is what percent of 44?

Translation: 11 = (x/100) (44)

Simplification: 11/44 = x/100
    1100/44 = x
    25 = x, which means 11 is 25 percent of 44.

This may seem obvious, so it's a point that's often missed: The key to percentage questions as well as all word problems is accurately translating the question into an algebraic expression that you can solve. That requires that you clearly understand the meaning of simple words like "of", "per", "percent", and "what".

Internet references

Math League: Percent and Probability (Percent, a fraction, a decimal, Estimating percents, Interest, Simple interest, Compound interest, Percent increase and decrease, Percent discount, Chances and probability, Possible outcomes of an event)

Related pages in this website

The next topic is Figuring the Percentage of Change.


The webmaster and author of this Math Help site is Graeme McRae.