# The Order of Operations

In algebra, there exists the following fundamental operators: **Parentheses, Exponents,
Division and Multiplication, Addition and Subtraction**. Many algebraic expressions
or equations you come across use more than one operator and their solutions will
be different depending on the order you carry out the diffrent operations. Keep
in mind that all expressions or equations are evaluated from left to right.

For example, given the expression:

One possible solution could be **36 - 4 x 6 = 192**, if we choose to evaluate
the expression as follows:

then

Alternatively, one can also evaluate the expression as follows:

Out of two possible solutions, only the second is correct.

In algebra, any given expression or equation with more than one operator is evaluated using a standard notation referred to as the order of operations which is represented by the acronym PEMDAS.

## PEMDAS

One easy way to remember the order of operations is to use the acronym **PEMDAS**
Observe that **PEMDAS** is formed using the first letter of each of the above
operators. (**P**arentheses, **E**xponents, **M**ultiplication and **D**ivision,
**A**ddition and **S**ubtraction).

Order of Operations is a standard used to denote which operators have precedence over the others and thus are solved first in any equation or expression.

## Examples of the Order of Operations

### Example 1

Evaluate the following

**Step 1**

First, evaluate whatever is in the parentheses:

**Step 2**

Next, evaluate the exponent:

**Step 3**

Evaluate any multiplication and division from left to right:

**Step 4**

Evaluate any addition and subtraction from left to right or which ever way makes it easier for you:

note that

is evaluated as

### Example 2

Solve for **x** in the equation below

**Step 1**

As always evaluate the expression within the parentheses first, since there is more than one operator in the parentheses, apply PEMDAS to the expression

**Step 2**

Divide both sides by 21

**Step 3**

### Example 3

Evaluate the following

**Step 1**

note that in the above expression, one can choose to divide first since that makes the computation easier

**Step 2**

### Example 4

Solve for **x** in the equation below

**Step 1**

**Step 2**

**Step 3**

**Step 3**

## Quiz on the Order of Operations

Step 1: Evaluate the inner parentheses first

Step 2: Evaluate the multiplication within the parentheses

Step 3: Evaluate the subtraction within the parentheses

Step 4: Finally evaluate the last multiplication