Basic Math and Pre-Algebra For Dummies (65 page)

You frequently work with decimals when dealing with money, metric measurements (see Chapter
15
), and food sold by the pound. The following problem requires you to add and subtract decimals, which I discuss in Chapter
11
. Even though the decimals may look intimidating, this problem is fairly simple to set up:

• Antonia bought 4.53 pounds of beef and 3.1 pounds of lamb. Lance bought 5.24 pounds of chicken and 0.7 pounds of pork. Which of them bought more meat, and how much more?
  

To solve this problem, you first find out how much each person bought:

You can already see that Antonia bought more than Lance. To find how much more, subtract:

• 7.63 – 5.94 = 1.69
  

So Antonia bought 1.69 pounds more than Lance.

When percents represent answers in polls, votes in an election, or portions of a budget, the total often has to add up to 100%. In real life, you may see such info organized as a pie chart (which I discuss in Chapter
17
). Solving problems about this kind of information often involves nothing more than adding and subtracting percents. Here's an example:

In a recent mayoral election, five candidates were on the ballot. Faber won 39% of the vote, Gustafson won 31%, Ivanovich won 18%, Dixon won 7%, Obermayer won 3%, and the remaining votes went to write-in candidates. What percentage of voters wrote in their selection?

The candidates were in a single election, so all the votes have to total 100%. The first step here is just to add up the five percentages. Then subtract that value from 100%:

Because 98% of voters voted for one of the five candidates, the remaining 2% wrote in their selections.

 In word problems, the word
of
almost always means multiplication. So whenever you see the word
of
following a fraction, decimal, or percent, you can usually replace it with a times sign.

When you think about it,
of
means multiplication even when you're not talking about fractions. For example, when you point to an item in a store and say, “I'll take three of those,” in a sense you're saying, “I'll take that one multiplied by three.”

The following examples give you practice turning word problems that include the word
of
into multiplication problems that you can solve with fraction multiplication.

When you understand that the word
of
means multiplication, you have a powerful tool for solving word problems. For instance, you can figure out how much you'll spend if you don't buy food in the quantities listed on the signs. Here's an example:

If beef costs $4 a pound, how much does
of a pound cost?

Here's what you get if you simply change the
of
to a multiplication sign:

So you know how much beef you're buying. However, you want to know the cost. Because the problem tells you that 1 pound = $4, you can replace 1 pound of beef with $4:

Now you have an expression you can evaluate. Use the rules of multiplying fractions from Chapter
10
and solve:

This fraction reduces to
. However, the answer looks weird because dollars are usually expressed in decimals, not fractions. So convert this fraction to a decimal using the rules I show you in Chapter
11
:

At this point, recognize that $2.5 is more commonly written as $2.50, and you have your answer.

Sometimes when you're sharing something such as a pie, not everyone gets to it at the same time. The eager pie-lovers snatch the first slice, not bothering to divide the pie into equal servings, and the people who were slower, more patient, or just not that hungry cut their own portions from what's left over. When someone takes a part of the leftovers, you can do a bit of multiplication to see how much of the whole pie that portion represents.

Consider the following example:

Jerry bought a pie and ate
of it. Then his wife, Doreen, ate
of what was left. How much of the total pie was left?