Basic Math and Pre-Algebra For Dummies (18 page)

Similarly, suppose you have 20 cherries and want to split them among four people. Here's how you represent this idea:

But you have to be careful when multiplying or dividing units by units. For example:

Neither of these equations makes any sense. In these cases, multiplying or dividing by units is meaningless.

In many cases, however, multiplying and dividing units is okay. For example, multiplying
units of length
(such as inches, miles, or meters) results in
square units.
For example,

You find out more about units of length in Chapter
15
. Similarly, here are some examples of when dividing units makes sense:

In these cases, you read the fraction slash (/) as
per:
slices of pizza
per
person or miles
per
hour. You find out more about multiplying and dividing by units in Chapter
15
, when I show you how to convert from one unit of measurement to another.

Sometimes you want to talk about when two quantities are different. These statements are called
inequalities.
In this section, I discuss six types of inequalities: ≠ (doesn't equal), < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), and ≈ (approximately equals).

The simplest inequality is ≠, which you use when two quantities are not equal. For example,

You can read ≠ as “doesn't equal” or “is not equal to.” Therefore, read
as “two plus two doesn't equal five.”

The symbol < means
less than.
For example, the following statements are true:  

•    4 < 5
  

   100 < 1,000
  

  2 + 2 < 5
  

Similarly, the symbol > means
greater than.
For example,

•   5 > 4
  

   100 > 99
  

  2 + 2 > 3
  

 The two symbols < and > are similar and easily confused. Here are two simple ways to remember which is which:

• Notice that the < looks sort of like an
  L.
  This
  L
  should remind you that it means
  less than.
  
• Remember that, in any true statement, the
  large
  open mouth of the symbol is on the side of the
  greater
  amount, and the
  small
  point is on the side of the
  lesser
  amount.
  

The symbol ≤ means
less than or equal to.
For example, the following statements are true:

Similarly, the symbol ≥ means
greater than or equal to.
For example,

 
The symbols ≤ and ≥ are called
inclusive inequalities
because they
include
(allow) the possibility that both sides are equal. In contrast, the symbols < and > are called
exclusive inequalities
because they
exclude
(don't allow) this possibility.

In Chapter
2
, I show you how rounding numbers makes large numbers easier to work with. In that chapter, I also introduce ≈, which means
approximately equals.

For example,