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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. (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

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

1. Evaluate the following

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

-48

2. Evaluate the following

1

3. Evaluate the following

-5

4. Evaluate the following

-1