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
5. Evaluate the following to 4 decimal places:
0.2589