Percentages made easy!

Required math knowledge:

This article assumes basic knowledge in algebra (like the significance of X as a variable), but hopefully I’ll be able to explain it in a way that makes sense to anyone who understands multiplication and division.

Boring Introduction:

Math problems of any kind can be made much easier to comprehend and solve if you follow a few steps. I’m serious! The people who are really good at math don’t do it all in their head! They will almost always follow these steps while trying to solve a problem! The steps are:

• Write it down in words.
• Draw a picture!
• Fill in the blanks with what you already know.

What’s that got to do with percentages?

Percentage problems qualify as math problems, so the above steps apply as well. I’m going to go into more detail with each step and even add another one that applies specifically to the problem of percentages.

So without further adieu, it’s time to get to the nitty gritty word problems!

The Problem

Sally took 50 apples to the farmers market and managed to sell 15 of them. What percentage of her apples did she sell?

Step 1. Write it down in words.

Don’t try to write out an equation right away. I don’t know about you, but I don’t think in mathematical equations. My native language is English, and I think in English. So in my case I would write the problem down in English. With percentage problems, there’s a very specific sentence structure you should use. This is what your sentence should look like, using the example given above:

“15 is what percent of 50?”

Step 2. Draw a picture.

Once you’ve got it out in easy-to-read sentence form, draw this picture on some scratch paper. The act of drawing a picture representing the problem really helps–especially with word problems–and this little sketch is what makes percentages so easy.

Step 3. Fill in the blanks with what you already know.

Now just look at the sentence you wrote down and use the numbers next to the word to find your formula. In other words, replace “is,” “of,” or “%” with the numbers that are next to them in the sentence. And for the value you don’t know (usually a “what” in your sentence), just put an X there. So since our sentence is “15 is what percent of 50?” we make the diagram like so.

Step 4. Solve for X.

See how that works? Now just solve for X to get the percentage. Solving for X in this example could be translated to this formula: x = 15 / 50 * 100, which comes out to x = 30. Don’t forget to add the % sign after you know what X is. Let’s rewrite our sentence now that we know the answer.

“15 is 30% of 50.”

This method can be used to find an answer as long as you know two of the numbers. It doesn’t matter what two numbers you know, as long as you know two of them you can find the other one. Take the following example sentences:

“What number is 30% of 50?”

“15 is 30% of what number?”

Can you see where to put the numbers in the equation shown in Step 2?

What if I need to know the ratio?

Ratios are actually nearly the same. Except all you need to do is solve the is/of part of the equation.