How to Think About Percentages

The Word “Percent”

It’s crucial to understand percents perfectly. Percentage problems are very common on all standardized tests, and for good reason. Having command of this subject will help you throughout your life. The way I encourage students to handle percents is to have a fool proof method of turning the words into simple math.

First, let’s consider the word “percent,” and break it down into its two parts. “Per” means “divided by.” Miles Per Hour is calculated by doing miles divided by hours. If you have 10 kids and 20 apples, you divide apples by kids to arrive at 2 kids per apple.

“Per” → Divided By

Now, let’s consider the second half of the word: “Cent.” “Cent” means 100. There are 100 cents in a dollar, 100 years in a century, 100 centimeters in a meter, 100 legs on a centipede.

“Cent” → 100

Combine them, and see that “percent” literally means “divided by 100.”

This may seem very obvious to some of you. Some schools teach this method for converting percents to fractions. For example, 50% is “fifty divided by one hundred,” or 50/100, which simplifies to one half.

The Three Ways Percent Questions are Phrased

  1. What is 27% of 85?
  2. 64 is what percent of 300?
  3. 75 is 30% of what?

The good news is, these are all essentially the same thing, just with a different unknown. Let’s learn how to translate these to simple math equations.

Before we jump into the questions, let’s do a little more vocabulary. The math equivalent of the word “is” is the equals sign. Two plus two is four.

“is” → “=”

That one seems obvious, but the next one is less so. The word “of” represents a multiplication sign. “One half of 6 is 3" → (1/2)*6=3

“of” → *

Only one word left to translate: “what.” “What” is the word we’re using to represent the unknown. In math, they use variables for this, most commonly the letter “x.”

“what” → x

Translating the Questions

  1. “What is 27% of 85?” → x = (27/100)*85

2. “64 is what percent of 300?” → 64 = (x/100)*300

3. “75 is 30% of what?” → 75 = (30/100)*x

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