Basic Math and Pre-Algebra For Dummies (22 page)

Even though this expression has some negative numbers, the only operations it contains are multiplication and division. So you can evaluate it in two steps from left to right (remembering the rules for multiplying and dividing with negative numbers that I show you in Chapter
4
):

Thus,
.

Often an expression contains

• At least one addition or subtraction operator
  
• At least one multiplication or division operator
  

I call these
mixed-operator expressions.
To evaluate them, you need some stronger medicine.

 Evaluate mixed-operator expressions as follows:

1. Evaluate the multiplication and division from left to right.
   
2. Evaluate the addition and subtraction from left to right.
   

For example, suppose you want to evaluate the following expression:

As you can see, this expression contains addition, multiplication, and division, so it's a mixed-operator expression. To evaluate it, start by underlining the multiplication and division in the expression:

Now evaluate what you've underlined from left to right:

At this point, you're left with an expression that contains only addition, so you can evaluate it from left to right:

Thus,
.

Here's what you need to know to evaluate expressions that have exponents (see Chapter
4
for info on exponents).

 Evaluate exponents from left to right
before
you begin evaluating Big Four operations (adding, subtracting, multiplying, and dividing).

The trick here is to turn the expression into a Big Four expression and then use what I show you earlier in “Applying order of operations to Big Four expressions.” For example, suppose you want to evaluate the following:

First, evaluate the exponent:

At this point, the expression contains only addition and subtraction, so you can evaluate it from left to right in two steps:

So
.