ORDER OF OPERATIONS

Definition Of Order Of Operations

Order of operation comes into play when a mathematical expression has more than one arithmetical operation.

Order of operations refers to the precedence of performing one arithmetical operation over another while working on a mathematical expression.

Here are the Rules:

1. Evaluate expressions inside parentheses.
2. Evaluate all powers
3. Perform all multiplications and/or divisions from left to right
4. Perform all additions and/or subtractions from left to right.

More About Order of Operations

Order of operations if not rigidly followed can lead to two different solutions to the same expression.
PEMDAS or BEDMAS help you remember order of operations.
PEMDAS - Please Excuse My Dear Aunt Sally
P - Parentheses
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction

Video Examples: Order Of Operations

BEDMAS
B - Brackets
E - Exponents
D - Division
M - Multiplication
A - Addition
S - Subtraction 

Examples of Order of Operations

2 + (25 - 4) × 20 ÷ 2
First do all operations inside parentheses
2 + (21) × 20 ÷ 2
Perform all multiplications and divisions, from left to right.
2 + 420 ÷ 2
2 + 210
Perform all additions and subtractions from left to right.
212

Solved Example on Order of Operations

Ques: Evaluate the variable expression 5x⁴ + 4 when x = 3 using order of operations.

Choices:

A. 419
B. 404
C. 409
D. 414
Correct Answer: C

Solution:

Step 1: 5x⁴ + 4[Original expression.] 
Step 2: = 5 × (3)⁴ + 4 [Substitute x = 3.] 
Step 3: = 5 × 81 + 4 [Evaluate power.] 
Step 4: = 405 + 4[Multiply 5 with 81.] 
Step 5: = 409 [Add.] 
Step 6: So, the value of 5x⁴ + 4 for x = 3 is 409.