We’ve spent a bit of time recently dealing with proportions, particularly proportion word problems. Today, we’re going to see how the idea of proportions ties into percentages. Better yet, we’re going to learn – relatively quickly – how to easily handle ANY math problem or real-life situation in which percentages play a role. All you have to do today is: 1. Memorize a very simple phrase. 2. Learn how to apply it. 3. Become really good at re-writing word problems into short sentences that simply ask the question you’re trying to find the answer to. (Oh, and it’s a really good idea to take some notes today. Seriously.)

You’re not alone if you find the following types of problems confusing or difficult:

You’re not alone if you find the following types of problems confusing or difficult: Despite what you might think, all of the problems shown here can be solved using the same method. This method is known by the following phrase: “Is Over Of = Percent Over 100” Written in “math,” it looks like this: IS = % OF 100

IS = % OF 100 The key to solving percentage problems is identifying the parts within each problem, because ANY problem becomes much easier to solve if you can identify the parts. There are three types of problems you can face:

As you read a problem involving percents, recognize that you’ll ALWAYS be given two pieces of data; your job is to find the third. The fourth piece of data – the “100” – is ALWAYS present in the equation. In other words, you’re never going to be solving for the value that belongs in the 100 spot in the equation, because 100 is always there. (Mr. Laney says it’s probably a really good idea to copy the chart above)

In most situations, the word “what” will show you which item in your “is over of” equation is unknown. In the first example above, “what percent” indicates that the variable goes in the “%” position. In the second example, “what number is” indicates that the variable belongs in the “IS” position. In the third example, “of what number” indicates that the variable belongs in the “OF” position. (Seriously, if you haven’t copied this chart yet, you’re going to struggle)

Let’s look at each of those three problems individually: Because the phrase “what percent” indicates the variable goes in the “%” location, all you have to do is decide where the 3 and the 4 belong. Read slowly; usually, the location for each piece of data is given away by the nearest word. “Three is what percent of 4?” Once you’ve identified the pieces, place them into your equation and cross-multiply to solve: 3 = x x = x = 300 X = 75; therefore, 3 is 75 percent of 4.

Let’s look at each of those three problems individually: Because the phrase “what number is” indicates the variable goes in the “IS” location, all you have to do is decide where the 75% and the 4 belong. “What number is 75% of 4?” Once you’ve identified the pieces, place them into your equation and cross-multiply to solve: x = x = 300 X = 3; therefore, 3 is 75 percent of 4.

Let’s look at each of those three problems individually: Because the phrase “of what number” indicates the variable goes in the “OF” location, all you have to do is decide where the 3 and the 75% belong. “Three is 75% of what number?” Once you’ve identified the pieces, place them into your equation and cross-multiply to solve: 3 = 75 x x = 300 x x = 300 X = 4; therefore, 3 is 75 percent of 4.

IS = % OF 100 The “Is Over Of” formula works great for word problems. You may have to re-word the problem to help you determine which pieces of data belong where, but with a bit of practice it should become fairly routine: Carbon makes up 18.5% of the human body by weight. How much carbon is contained in a person weighing 145 pounds? Read slowly; recognize that the % sign is a giveaway that 18.5 belongs in the % position. Plus, the 100 is ALWAYS PRESENT. Where does the 145 belong, and where in the equation will you place the variable?

IS = % OF 100 Read carefully, and you can place everything properly. Carbon makes up 18.5% of the human body by weight. How much carbon is contained in a person weighing 145 pounds? Additionally, you can re-word the word problem into a much shorter question: What is 18.5% of 145 pounds? x = x = x = pounds

IS = % OF 100 Let’s try another one: Caitlin made some Valentine’s Day cookies using red and blue M&M’s The recipe called for 40% of the M&M’s to be blue. If she uses a total of 80 M&M’s, how many RED ones does she need? We know that 40% of the M&M’s are blue; that means the other 60% are red, and the problem is asking us to determine how many red M&M’s we need. After reading the word problem, we can re-word it into a short, essential question: What is 60% of 80 total M&M’s?

IS = % OF 100 Caitlin made some Valentine’s Day cookies using red and blue M&M’s The recipe called for 40% of the M&M’s to be blue. If she uses a total of 80 M&M’s, how many RED ones does she need? What is… 60%... of 80 total M&M’s? x = x = 4800 x = of Caitlin’s M&M’s need to be red.

IS = % OF 100 Try your hand at this one: In a typical year, your parents spend $4,800 on food. If you eat $1,500 of this total, what percentage of your family’s food are you eating? Take a look at the question. You are being asked to find the percentage, so clearly the variable will go in the “%” position. Now… where does the $1,500 and $4,800 go? Re-word the problem into a short, essential question: $1,500 is what percent of $4,800?

IS = % OF 100 In a typical year, your parents spend $4,800 on food. If you eat $1,500 of this total, what percentage of your family’s food are you eating? $1,500 is…. what percent…. of $4,800? 1500 = x x = x = You are eating 31.25% of your family’s food. You pig.

It takes a bit of practice, but once you get the hang of it you should be able to handle any percentage problem thrown at you. Remember the three steps: 1. Memorize a simple phrase (“is over of = % over 100”). 2. Learn how to identify the pieces of data in the problem. 3. Re-write word problems into short, essential questions. One final thought: CHECK YOUR ANSWER FOR REASONABLENESS! If it isn’t reasonable, you’ve got your data in improper places. Try moving some things around in your equation in order to come up with a more logical answer. A five-second check to ask yourself “does this make sense” will usually eliminate ALL errors. If it isn’t reasonable, you’ve got your data in improper places. Try moving some things around in your equation in order to come up with a more logical answer. A five-second check to ask yourself “does this make sense” will usually eliminate ALL errors.