Basic Math and Pre-Algebra For Dummies (104 page)

With the chart filled in like this, you can begin to set up your equation. First, set up a word equation, as follows:

• Jake tomorrow + Kyle tomorrow + Mina tomorrow + Suzanne tomorrow + Victor tomorrow = 174
  

Now just substitute information from the chart into this word equation to set up your equation:

• 17 +
  v
  + 5 + 2
  v
  + 5 + 17 + 17 +
  v
  + 8 +
  v
  + 5 = 174
  

As always, begin solving by isolating the algebraic terms:

• v
  + 2
  v
  +
  v
  +
  v
  = 174 – 17 – 5 – 5 – 17 – 17 – 8 – 5
  

Next, combine like terms:

• 5
  v
  = 100
  

Finally, to get rid of the coefficient in the term 5
v,
divide both sides by 5:

You now know that Victor's total distance up to
today
is 20 miles. With this information, you substitute 20 for
v
and fill in the chart, as follows:

• Today 	Tomorrow (Today + 5)
  Jake 	37 	42
  Kyle 	40 	45
  Mina 	12 	17
  Suzanne 	40 	45
  Victor 	20 	25

The
Today
column contains the answers to the question the problem asks. To check this solution, make sure that every statement in the problem is true. For example, tomorrow the five people will have run a total of 174 miles because

• 42 + 45 + 17 + 45 + 25 = 174
  

Copy down this problem, close the book, and work through it for practice.

Part VI

 Math is full of important concepts. To discover ten of the most interesting, go to
www.dummies.com/extras/basicmathandprealgebra
.

In this part…

• Discover tricks to help you avoid making common mathematical mistakes
  
• Expand your understanding of math by learning how to distinguish between different kinds of numbers: natural numbers, integers, rational (and irrational) numbers, algebraic numbers, and more
  

Chapter 24

In This Chapter

Knowing the multiplication table once and for all

Understanding negative numbers

Distinguishing factors and multiples

Working confidently with fractions

Seeing what algebra is really all about

The ten little math demons I cover in this chapter plague all sorts of otherwise smart, capable folks like you. The good news is that they're not as big and scary as you may think, and they can be dispelled more easily than you may have dared believe. Here, I present ten common math demons, with a short explanation to set them on a path away from you.

A sketchy knowledge of multiplication can really hold back an otherwise good math student. Here's a quick quiz: the ten toughest problems from the multiplication table.

Can you do this, 10 for 10, in 20 seconds? If so, you're a multiplication whiz. If not, flip to Chapter
3
and work through my short, sweet, and simple program for nailing the multiplication table once and for all!

It's easy to get confused when adding and subtracting negative numbers. To begin, think of adding a number as moving
up
and subtracting a number as moving
down.
For example:

• 2 + 1 – 6

  means

  up 2, up 1, down 6

So if you go
up
2 steps, then
up
1 more step, and then
down
6 steps, you've gone a total of 3 steps
down;
therefore, 2 + 1 – 6 = –3.

Here's another example:

• –3 + 8 – 1

  means

  down 3, up 8, down 1

This time, go
down
3 steps, then
up
8 steps, and then
down
1 step, you've gone a total of 4 steps
up;
therefore, –3 + 8 – 1 = 4.

 You can turn every problem involving negative numbers into an up-and-down example. The way to do this is by combining adjacent signs:

• Combine a plus and minus as a
  minus
  sign.
  
• Combine two minus signs as a
  plus
  sign.
  

For example:

• –5 + (–3) – (–9)
  

In this example, you see a plus sign and a minus sign together (between the 5 and the 3), which you can combine as a minus sign. You also see two minus signs (between the 3 and the 9), which you can combine as a plus sign:

• –5 – 3 + 9

  means

  down 5, down 3, up 9

This technique allows you use your up-and-down skills to solve the problem:
Down
5 steps, then
down
3 steps, and
up
9 steps leaves you 1 step
up;
therefore, –5 + (–3) – (–9) = 1.

See Chapter
4
for more on adding and subtracting negative numbers.

When you multiply or divide a positive number by a negative number (or vice versa), the answer is always negative. For example:

When you multiply two negative numbers, remember this simple rule: Two negatives always cancel each other out and equal a positive.

For more on multiplying and dividing negative numbers, see Chapter
4
.

Lots of students get factors and multiples confused because they're so similar. Both are related to the concept of divisibility. When you divide one number by another and the answer has no remainder, the first number is
divisible
by the second. For example:

When you know that 12 is divisible by 3, you know two other things as well:

• 3 is a factor of 12

  and

  12 is a multiple of 3