Basic Math and Pre-Algebra For Dummies (64 page)

As another example, suppose you're faced with this percent problem:

What percent of 250 is 375?

To begin, change the
of
into a multiplication sign and the percent into a decimal.

Notice here that, because I don't know the percent, I change the word
percent
to × 0.01. Next, change
is
to an equals sign and
what
to the letter
n
:

Consolidate the equation and then multiply:

Now divide both sides by 2.5:

Therefore, the answer is 150 — so 150% of 250 is 375.

Here's one more problem: 49 is what percent of 140? Begin, as always, by translating the problem into words:

Simplify the equation:

49 =
n
× 1.4

Now divide both sides by 1.4:

49 ÷ 1.4 =
n
× 1.4 ÷ 1.4

Again, multiplication and division by the same number allows you to cancel on the left side of the equation and complete the problem:

49 ÷ 1.4 =
n

35 =
n

Therefore, the answer is 35, so 49 is 35% of 140.

Chapter 13

In This Chapter

Adding and subtracting fractions, decimals, and percents in word equations

Translating the word
of
as multiplication

Changing percents to decimals in word problems

Tackling business problems involving percent increase and decrease

In Chapter
6
, I show you how to solve word problems (also known as story problems) by setting up word equations that use the Big Four operations (adding, subtracting, multiplying, and dividing). In this chapter, I show you how to extend these skills to solve word problems with fractions, decimals, and percents.

First, I show you how to solve relatively easy problems, in which all you need to do is add or subtract fractions, decimals, or percents. Next, I show you how to solve problems that require you to multiply fractions. Such problems are easy to spot because they almost always contain the word
of
. After that, you discover how to solve percent problems by setting up a word equation and changing the percent to a decimal. Finally, I show you how to handle problems of percent increase and decrease. These problems are often practical money problems in which you figure out information about raises and salaries, costs and discounts, or amounts before and after taxes.

Certain word problems involving fractions, decimals, and percents are really just problems in adding and subtracting. You may add fractions, decimals, or percents in a variety of real-world settings that rely on weights and
measures — such as cooking and carpentry. (In Chapter
15
, I discuss these applications in depth.)

To solve these problems, you can use the skills that you pick up in Chapters
10
(for adding and subtracting fractions),
11
(for adding and subtracting decimals), and
12
(for adding and subtracting percents).

You may have to add or subtract fractions in problems that involve splitting up part of a whole. For example, consider the following:

• Joan ate
  of a pizza, Tony ate
  , and Sylvia ate
  . What fraction of the pizza was left when they were finished?
  

In this problem, just jot down the information that's given as word equations:

These fractions are part of one total pizza. To solve the problem, you need to find out how much all three people ate, so form the following word equation:

• all three = Joan + Tony + Sylvia
  

Now you can substitute as follows:

Chapter
10
gives you several ways to add these fractions. Here's one way:

However, the question asks what fraction of the pizza was left after they finished, so you have to subtract that amount from the whole:

Thus, the three people left
of a pizza.