Basic Math and Pre-Algebra For Dummies (97 page)

• = 7(2)
  xx
  = 14
  xx
  

Remember that
x
²
is shorthand for
xx
, so you can write the answer more efficiently:

• =14
  x
  ²
  

Here's another example. Multiply all three coefficients together and gather up the variables:

As you can see, the exponent 3 that's associated with
x
is just the count of how many
x
's appear in the problem. The same is true of the exponent 2 associated with
y.

 A fast way to multiply variables with exponents is to add the exponents together. For example:

In this example, I added the exponents of the
x
's (4 + 2 + 6 = 12) to get the exponent of
x
in the expression. Similarly, I added the exponents of the
y
's (3 + 5 + 1 = 9 — don't forget that
y
=
y
¹
!) to get the exponent of
y
in the expression.

It's customary to represent division of algebraic expressions as a fraction instead of using the division sign (÷). So division of algebraic terms really looks like reducing a fraction to lowest terms (see Chapter
9
for more on reducing).

To divide one algebraic term by another, follow these steps:

1. Make a fraction of the two terms.
   

   Suppose you want to divide 3
   xy
   by 12
   x
   ²
   . Begin by turning the problem into a fraction:
   

   

2. Cancel out factors in coefficients that are in both the numerator and the denominator.
   

   In this case, you can cancel out a 3. Notice that when the coefficient in
   xy
   becomes 1, you can drop it:
   

   

3. Cancel out any variable that's in both the numerator and the denominator.
   

   You can break
   x
   ²
   out as
   xx:
   

   

   Now you can clearly cancel an
   x
   in both the numerator and the denominator:
   

   

   As you can see, the resulting fraction is really a reduced form of the original.
   

As another example, suppose you want to divide –6
x
²
yz
³
by –8
x
²
y
²
z
. Begin by writing the division as a fraction:

First, reduce the coefficients. Notice that, because both coefficients were originally negative, you can cancel out both minus signs as well:

Now you can begin canceling variables. I do this in two steps, as before:

At this point, just cross out any occurrence of a variable that appears in both the numerator and the denominator:

 
You can't cancel out variables or coefficients if either the numerator or the denominator has more than one term in it. This is a very common mistake in algebra, so don't let it happen to you!