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Three Common Questions

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There are three basic types of questions that you'll run into with percentages. If you understand the process for translating an English sentence into a mathematical equation they're all easy to work with. The three forms look like this:

10 is what percentage of 50?
What is 30% of 18?
What percentage of 19 is 38?

There are a few simple rules for translating English to math that you need to remember to make these problems simple:

  1. "what" equals "x" or the variable that you're going to solve for
  2. "is" equals "="
  3. "of" equals "·" or multiplication

Let's apply those conversions to the three questions I asked at the beginning of the page.

Example 1

10 is  what percentage  of  50?
10 =  x  ·  50

Notice how I converted each word or phrase literaly. That gave me an equation that I can solve:

10 = x · 50
x = 10 / 50 = .2

Now, if you look back at the original question, you'll see that we're looking for a percentage but what we've got so far is the answer's decimal version. The last step would be to convert .2 to its equivalent percentage by multiplying it by 100. This gives us .2 · 100% = 20% for our final answer.

Example 3

 19  is  38%  of  what number?
19 =  .38  · x

Solving that equation gives us:

19 = .38 · x
x = 19 / .38
x = 50

Example 2

What is  30%  of  18?
x =  30%  ·  18

I wrote that out with 30% in the equation but remember that you can't mix and match percentages and numbers and you especially can't multiply percentages and numbers. To get an equation that we can solve, we need to convert the 30% to a decimal by dividing its number part by 100: 30 / 100 = .3.

x = .3 · 18
x = 5.4

The original question was asking for a number (not a percentage) and that's what we've found so 5.4 would be our final answer.

Quick Tip - Rounding

Any time you're doing division where your answer is a decimal, sooner or later, you'll have to decide where to round your result. I like to go out to two decimal places but you should be sure to follow the directions in a question or any standing directions set up by a class' instructor.


Dyanmic Practice - Three Basic Questions


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