Basic Math and Pre-Algebra For Dummies (23 page)

In math, parentheses — ( ) — are often used to group together parts of an expression. When it comes to evaluating expressions, here's what you need to know about parentheses.

 To evaluate expressions that contain parentheses,

1. Evaluate the contents of parentheses from the inside out.
   
2. Evaluate the rest of the expression.
   

Similarly, suppose you want to evaluate
. This expression contains two sets of parentheses, so evaluate these from left to right. Notice that the first set of parentheses contains a mixed-operator expression, so evaluate this in two steps, starting with the division:

Now evaluate the contents of the second set of parentheses:

Now you have a mixed-operator expression, so evaluate the multiplication (
) first:

• = 4 + −15
  

Finally, evaluate the addition:

• = −11
  

So
.

As another example, try this out:

Start by working with
only
what's inside the parentheses. The first part to evaluate there is the exponent,
:

Continue working inside the parentheses by evaluating the division
:

Now you can get rid of the parentheses altogether:

At this point, what's left is an expression with an exponent. This expression takes three steps, starting with the exponent: