Basic Math and Pre-Algebra For Dummies (27 page)

Now you can jot this information down, as always:

• Jezebel = $498.65
  

The question at the end of the problem asks you to find out how much money the two women have all together. Here's how to represent this question as an equation:

• Effie + Jezebel = ?
  

You can plug information into this equation:

• $732.84 + $498.65 = ?
  

Again, because the numbers are large, you probably have to stop to do the math:

So all together, Aunt Effie and Aunt Jezebel have $1,231.49.

As you can see, the procedure for solving this problem is basically the same as for the simpler problems in the earlier sections. The only difference is that you have to stop to do some addition and subtraction.

When the going gets tough, knowing the system for writing word equations really becomes helpful. Here's a word problem that's designed to scare you off — but with your new skills, you're ready for it:

• Four women collected money to save the endangered Salt Creek tiger beetle. Keisha collected $160, Brie collected $50 more than Keisha, Amy
  collected twice as much as Brie, and together Amy and Sophia collected $700. How much money did the four women collect all together?
  

If you try to do this problem all in your head, you'll probably get confused. Instead, take it line by line and just jot down word equations as I discuss earlier in this chapter.

First, “Keisha collected $160.” So jot down the following:

• Keisha = 160
  

Next, “Brie collected $50 dollars more than Keisha,” so write

• Brie = Keisha + 50
  

After that, “Amy collected twice as much as Brie”:

• Amy = Brie × 2
  

Finally, “together, Amy and Sophia collected $700”:

• Amy + Sophia = 700
  

That's all the information the problem gives you, so now you can start working with it. Keisha collected $160, so you can plug in 160 anywhere you find Keisha's name:

• Brie = 160 + 50 = 210
  

Now you know how much Brie collected, so you can plug this information into the next equation:

• Amy = 210 × 2 = 420
  

This equation tells you how much Amy collected, so you can plug this number into the last equation:

• 420 + Sophia = 700
  

To solve this problem, change it from addition to subtraction using inverse operations, as I show you in Chapter
4
:

• Sophia = 700 − 420 = 280
  

Now that you know how much money each woman collected, you can answer the question at the end of the problem:

• Keisha + Brie + Amy + Sophia = ?
  

You can plug in this information easily:

• 160 + 210 + 420 + 280 = 1,070
  

So you can conclude that the four women collected $1,070 all together.

Here's one final example putting together everything from this chapter. Try writing down this problem and working it through step by step on your own. If you get stuck, come back here. When you can solve it from beginning to end with the book closed, you'll have a good grasp of how to solve word problems:

• On a recent shopping trip, Travis bought six shirts for $19.95 each and two pairs of pants for $34.60 each. He then bought a jacket that cost $37.08 less than he paid for both pairs of pants. If he paid the cashier with three $100 bills, how much change did he receive?
  

On the first read-through, you may wonder how Travis found a store that prices jackets that way. Believe me — it was quite a challenge. Anyway, back to the problem. You can jot down the following word equations:

The numbers in this problem are probably longer than you can solve in your head, so they require some attention:

With this done, you can fill in some more information:

Now you can plug in $69.20 for
pants:

• jacket = $69.20 − $37.08
  

Again, because the numbers are long, you need to solve this equation separately:

This equation gives you the price of the jacket:

• jacket = $32.12
  

Now that you have the price of the shirts, pants, and jacket, you can find out how much Travis spent:

• amount Travis spent = $119.70 + $69.20 + $32.12
  

Again, you have another equation to solve:

So you can jot down the following:

• amount Travis spent = $221.02
  

The problem is asking you to find out how much change Travis received from $300, so jot this down:

• change = $300 − amount Travis spent
  

You can plug in the amount that Travis spent:

• change = $300 − $221.02
  

And do just one more equation:

So you can jot down the answer:

• change = $78.98
  

Therefore, Travis received $78.98 in change.

Chapter 7

In This Chapter

Finding out whether a number is divisible by 2, 3, 5, 9, 10, or 11

Seeing the difference between prime numbers and composite numbers

When one number is
divisible
by another, you can divide the first number by the second number without getting a remainder (see Chapter
3
for details on division). In this chapter, I explore divisibility from a variety of angles.

To start, I show you a bunch of handy tricks for discovering whether one number is divisible by another without actually doing the division. (In fact, you don't find long division anywhere in this chapter!) After that, I talk about prime numbers and composite numbers (which I introduce briefly in Chapter
1
).

This discussion, plus what follows in Chapter
8
, can help make your encounter with fractions in Part
III
a lot friendlier.

As you begin to work with fractions in Part
III
, the question of whether one number is divisible by another comes up a lot. In this section, I give you a bunch of time-saving tricks for finding out whether one number is divisible by another without actually making you do the division.

Every number is divisible by 1. As you can see, when you divide any number by 1, the answer is the number itself, with no remainder:

Similarly, every number (except 0) is divisible by itself. Clearly, when you divide any number by itself, the answer is 1:

 You can't divide any number by 0. Mathematicians say that dividing by 0 is
undefined.

You can tell whether a number is divisible by 2, 5, 10, 100, or 1,000 simply by looking at how the number ends — no calculations required.

Every even number — that is, every number that ends in 2, 4, 6, 8, or 0 — is divisible by 2. For example, the following bolded numbers are divisible by 2:

Every number that ends in either 5 or 0 is divisible by 5. The following bolded numbers are divisible by 5:

Every number that ends in 0 is divisible by 10. The following bolded numbers are divisible by 10:

Every number that ends in 00 is divisible by 100:

And every number that ends in 000 is divisible by 1,000:

In general, every number that ends with a string of 0s is divisible by the number you get when you write 1 followed by that many 0s. For example,

• 900,000 is divisible by 100,000.
  
• 235,000,000 is divisible by 1,000,000.
  
• 820,000,000,000 is divisible by 10,000,000,000.
  

 When numbers start to get this large, mathematicians usually switch over to
scientific notation
to write them more efficiently. In Chapter
14
, I show you how to work with scientific notation.

Sometimes you can check divisibility by adding up all or some of the digits in a number. The sum of a number's digits is called its
digital root.
Finding the digital root of a number is easy, and it's handy to know.