# Prealgebra: Operations

### Order of Operations

An expression represents a number. For example, 6 - 2 is an expression that represents the number 4, and 3×5 is an expression that represents the number 15. This section will discuss how to find the unique number that each expression represents.

Consider the expression 2 + 4×3 . How might one search for the answer? One way is to start by adding 2 + 4 = 6 and then multiply 6×3 = 18 . Another way is to first multiply 4×3 = 12 and then add 2 + 12 = 14 . Only one of these answers can be correct. So which is it?

The solution lies in following the Order of Operations. This rule specifies an order in which to add, subtract, multiply and divide so that everyone can look at an expression and get the same correct answer.

There are three steps to finding the answer, or to evaluating the expression, as specified by the order of operations:

Step 1. Carry out the operations within parentheses.
Step 2. Multiply and divide (it does not matter which comes first).
Step 3. Add and subtract (it does not matter which comes first).

For example, to evaluate (3 + 2)×5 + (7 - 3) , go through the steps:

Step 1 (Parentheses). (3+2)×5 + (7-3) = 5×5 + 4
Step 2 (Multiplication and Division). 5×5 +4 = 25 + 4
Step 3 (Addition and Subtraction). 25+4 = 29
Thus, (3 + 2)×5 + (7 - 3) = 29

In the example at the beginning of this section, 2 + 4×3 , the steps are:

Step 1. 2 + 4×3 = 2 + 4×3 (There are no parentheses)
Step 2. 2 + 4×3 = 2 + 12
Step 3. 2+12 = 14
Thus, 2 + 4×3 = 14 .

Sometimes the expression within the parentheses might contain a combination of multiplication, division, addition, and subtraction, or even more parentheses. If this is the case, go through the steps in the order of operations for the expression within the parentheses.

For example, to evaluate (12 - 6/(3 - 1))/(7 - 4) + 2 :

Step 1.1 (12 - 6/(3-1))/(7 - 4) + 2 = (12 - 6/2)/(7 - 4) + 2
Step 1.2 (12 - 6/2)/(7 - 4) + 2 = (12 - 3)/(7 - 4) + 2
Step 1.3 (12-3)/(7-4) + 2 = 9/3 + 2
Step 2. 9/3 +2 = 3 + 2
Step 3. 3+2 = 5

Here are some more examples:

Example 1. 12/(6 - 2) - (3×1) = ?

Step 1. 12/(6-2)-(3×1) = 12/4-3
Step 2. 12/4 -3 = 3 - 3
Step 3. 3-3 = 0
Example 2. (11 - 3×2) + 2×3×4 - (3 + 2) = ?
Step 1. 1. (11 - 3×2) + 2×3×4 - (3 + 2) = (11 - 3×2) + 2×3×4 - (3 + 2)
2. (11 - 3×2) + 2×3×4 - (3 + 2) = (11 - 6) + 2×3×4 - (3 + 2)
3. (11-6) + 2×3×4 - (3+2) = 5 +2×3×4 - 5
Step 2. 5 + 2×3×4 -5 = 5 + 24 - 5
Step 3. 5+24-5 = 24

## Take a Study Break

### Star Trek gets SEXY

Chris Pine and Zoe Saldana heat up the red carpet!

### Are you afraid of relationships?

Auntie SparkNotes can help!

### Sexy starlet style

See every single look from the Met Gala!

### Geeky Actors: Then and Now

Travel back in time!

### Villains We Want These Actresses to Play

From super cute to super bad!

### 10 Movies Better Than Their Books

What do you think?

### How To Look Like J-Law...

When you don't look like J-Law.

### 12 Scientific Inaccuracies in Into Darkness

What did Star Trek get wrong?

## The Book

### Read What You Love, Anywhere You Like

Get Our FREE NOOK Reading Apps