Work With Percentages

The first thing to understand is that there are two major categories of percentage problems: straight comparison questions (such as, "35 is 5% of what number?") and increase/decrease questions (like, "if a blouse that cost $45 originally is on sale at 20% off, what is the new price?). The increase/ decrease kind are complicated enough to require a separate Wikihow article, so let's focus on just the straight comparison for right now.

The other thing to know is that there are two major approaches to these questions. One is based on an equation involving decimals, and the other relies on proportions. I'm going to stick with the method that's based on the decimal equation, which is: % x (whole amount) = (partial amount). This equation can be rearranged like this: % = (partial amt) / (whole amt). It can also be written like this: (whole amt) = (partial amt) / %. Which arrangement you need depends on which kind of problem you have.

The Place to Start

Your first task is to figure out what kind of problem is in front of you. In a straight comparison situation, there are three styles of problems. The first style is the "no percent" question. Those would sound like: "what percent of 25 is 16?" or "8 is what percent of 32?". The second style is the "no entire amount" question. Those would be phrased like: "15 is 6% of what number?" or "78% of what number is 20?". The third style is the "no partial amount" question, which would sound like: "What is 52% of 49?" or "14% of 225 is how much?"

Steps

Solving an "Unknown Percent" Question

If you do not see a number marked by a % (or possibly the word "percent"), then this is almost certainly the "no percent" type of question.

  1. Decide which of the other numbers is the "whole amount" and which is the "partial amount". For example, a problem that says "8 is what percent of 32?" indicates that the 32 is the whole amount and the 8 is the partial. What tips this off: the 8 connects directly to the "is", while the 32 connects directly to the "of".
  2. Use the equation % = (partial)/(whole). So on the calculator, punch in the partial amount, hit divide, enter the whole, and hit equals.
  3. This will give you a decimal, which you convert into a percentage by moving the decimal point two places to the right.
    • Example: "8 is what percent of 32?". Take 8, divide by 32, hit equals; get 0.25; convert that to 25%.
    • Example: "what percent of 25 is 16?". Enter 16, divide by 25, hit equals; get 0.64; convert to 64%.
    • Example: "what percent of 12 is 45?". Enter 45, divide by 12, hit equals; get 3.75; convert to 375%. (Answers larger than 100%, while rare, are acceptable).
    • Example: "9 is what percent of 250?". Enter 9, divide by 250, hit equals; get 0.036; convert to 3.6%.

Solving an "Unknown Entire Amount" Problem

Let's say you have a percent. You now need to decide if the question is the "no whole amount" style or the "unknown partial amount" style. This is a trickier call to make and much depends on the context of the question.

  1. Look for the markers "is" and "of" and "what". "Is" tends to be associated with the partial amount, while "of" is paired with the entire amount. The word "what" indicates the unknown.
    • Example: A question says, "what is 10% of 16?" The phrase "what is" indicates that the partial amount is unknown. The phrase "of 16" indicates that 16 is the whole amount. This is an "unknown partial amount" problem.
    • Example: A question says, "15 is 25% of what number?" The phrase "of what" means that the entire amount is unknown, but the phrase "15 is" shows that 15 is the partial amount. This would be an "unknown entire amount" problem.
  2. Let's assume you have an "unknown entire amount" problem, like "15 is 25% of what number?". First of all, change the percent into a decimal --- 0.25 instead of 25%, 1.38 instead of 138%, 0.07 instead of 7%, etc.
  3. Use the equation: (whole amt) = (partial) / %.
  4. Using your calculator, enter the partial amount, hit divide, enter the percentage decimal, and hit equals.
    • Example: "15 is 25% of what number?". Grab your calculator, enter 15, hit the divide key, enter 0.25, hit equals. The answer is 60. You're done. (Notice, it's just 60. Not 60%.)
    • Example: "32% of what number is 16?". Enter 16, hit divide, enter 0.32, hit equals; the answer is 50.
    • Example: "125% of what number is 80?". Enter 80, hit divide, enter 1.25, hit equals; the answer is 64.
    • Example: "6 is 7.5% of what number?". Enter 6, hit divide, enter .075, hit equals; the answer is 80.

Solving an "Unknown Partial Amount" Problem

  1. Look for the "is", "of", and "what" (or possibly "how much"). If the "is" and the "what" are closely associated, like in the question "what is 10% of 16?", then you have a "no partial amount" problem.
  2. Here's what to do: Change the percentage back to a decimal, so 32% is 0.32 and 75% is 0.75 and 150% is 1.5 and 6% is 0.06, and so forth.
  3. Use the equation: % x (whole amt) = (partial amt). In other words, you multiply the percent with the entire amount.
    • Example: "what is 10% of 16?". Enter 0.10, hit multiply, enter 16, hit equals. The answer is 1.6 (notice, no % sign on the answer).
    • Example: "230% of 40 is what?". Enter 2.3, hit multiply, enter 40, hit equals. The answer: 92.
    • Example: "how much is 37% of 200?". Enter 0.37, hit multiply, enter 200, hit equals. Answer: 74.



Tips

  • To summarize, you either: A) divide the partial BY the whole; or, B) you divide the partial BY the percent; or, C) you multiply the whole by the percent. Which one you use depends on which numbers you have.
  • Apply the TLAR --- That Looks About Right --- principle. Make sure that your answer is reasonable.
  • With the "no partial amount" style of problem, the order of the multiplication does not matter. You could solve "230% of 45" with the sequence 2.3 x 45 = or with 45 x 2.3 =
  • The only time you multiply is if you have the % and the whole amount. Otherwise, you're dividing.

Warnings

  • The order of division is vitally important! In both of the kinds of questions that are solved with division, the partial amount goes into the calculator first.
  • Most calculators have a percent key. Its purpose is to move the decimal point twice to the left, turning 35% into 0.35, and 325% into 3.25, and 6% into 0.06, and so on. I advise AGAINST using this key because I find that most of my students move the decimal point themselves, then hit the % key as well, and everything gets screwed up.

Things You'll Need

  • A calculator.

or a sheet of paper

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