**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**-**P**lease**E**xcuse**M**y**D**ear**A**unt**S**ally

P - Parentheses

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

**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**

Evaluate the variable expression 5

x^{4}+ 4 whenx= 3 using order of operations.

Choices:

A. 419

B. 404

C. 409

D. 414

Correct Answer: C

Solution:

Step 1:5x^{4}+ 4 [Original expression.]

Step 2:= 5 × (3)^{4}+ 4 [Substitutex= 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 5x^{4}+ 4 forx= 3 is 409.

**Related Terms for Order of Operations**

- Addition
- Subtraction
- Multiplication
- Division
- Exponents
- BEDMAS
- PEMDAS