Basic Math and Pre-Algebra For Dummies (63 page)

Here's a trick that makes certain tough-looking percent problems so easy that you can do them in your head. Simply move the percent sign from one number to the other and flip the order of the numbers.

Suppose someone wants you to figure out the following:

• 88% of 50
  

Finding 88% of anything isn't an activity anybody looks forward to. But an easy way of solving the problem is to switch it around:

• 88% of 50 = 50% of 88
  

This move is perfectly valid, and it makes the problem a lot easier. It works because the word
of
really means multiplication, and you can multiply either
backward or forward and get the same answer. As I discuss in the preceding section, “Figuring out simple percent problems,” 50% of 88 is simply half of 88:

• 88% of 50 = 50% of 88 = 44
  

As another example, suppose you want to find

• 7% of 200
  

Again, finding 7% is tricky, but finding 200% is simple, so switch the problem around:

• 7% of 200 = 200% of 7
  

In the preceding section, I tell you that, to find 200% of any number, you just multiply that number by 2:

You can solve a lot of percent problems, using the tricks I show you earlier in this chapter. For more difficult problems, you may want to switch to a calculator. If you don't have a calculator at hand, solve percent problems by turning them into decimal multiplication, as follows:

1. Change the word
   of
   to a multiplication sign and the percent to a decimal (as I show you earlier in this chapter).
   

   Suppose you want to find 35% of 80. Here's how you start:
   

   

2. Solve the problem using decimal multiplication (see Chapter
   11
   ).
   

   Here's what the example looks like:
   

   

   So 35% of 80 is 28.
   

In the preceding section, “Solving Percent Problems,” I give you a few ways to find any percent of any number. This type of percent problem is the most common, which is why it gets top billing.

But percents crop up in a wide range of business applications, such as banking, real estate, payroll, and taxes. (I show you some real-world applications when I discuss word problems in Chapter
13
.) And depending on the situation, two other common types of percent problems may present themselves.

In this section, I show you these two additional types of percent problems and how they relate to the type you now know how to solve. I also give you a simple tool to make quick work of all three types.

Earlier in this chapter, I show you how to solve problems that look like this:

• 50% of 2 is ?
  

The answer, of course, is 1. (See “Solving Percent Problems” for details on how to get this answer.) Given two pieces of information — the percent and the number to start with — you can figure out what number you end up with.

Now suppose instead that I leave out the percent but give you the starting and ending numbers:

• ? % of 2 is 1
  

You can still fill in the blank without too much trouble. Similarly, suppose that I leave out the starting number but give the percent and the ending number:

• 50% of ? is 1
  

Again, you can fill in the blank.

If you get this basic idea, you're ready to solve percent problems. When you boil them down, nearly all percent problems are like one of the three types I show in Table 
12-1
.

Table 12-1 
The Three Main Types of Percent Problems

In each case, the problem gives you two of the three pieces of information, and your job is to figure out the remaining piece. In the next section, I give you a simple tool to help you solve all three of these types of percent problems.

 Here's how to solve any percent problem:

1. Change the word
   of
   to a multiplication sign and the percent to a decimal (as I show you earlier in this chapter).
   

   This step is the same as for more straightforward percent problems. For example, consider this problem:
   

   • 60% of what is 75?
     

   Begin by changing as follows:
   

   • 

2. Turn the word
   is
   to an equals sign and the word
   what
   into the letter
   n
   .
   

   Here's what this step looks like:
   

   • 

   This equation looks more normal, as follows:
   

   

3. Find the value of
   n
   .
   

   Technically, the last step involves a little bit of algebra, but I know you can handle it. (For a complete explanation of algebra, see Part V of this
   book.) In the equation,
   n
   is being multiplied by 0.6. You want to “undo” this operation by
   dividing
   by 0.6 on both sides of the equation:
   

   

   Almost magically, the left side of the equation becomes a lot easier to work with because multiplication and division by the same number cancel each other out:
   

   

   Remember that
   n
   is the answer to the problem. If your teacher lets you use a calculator, this last step is easy; if not, you can calculate it using some decimal division, as I show you in Chapter
   11
   :
   

   

   Either way, the answer is 125 — so 60% of 125 is 75.