Order Of Operations – Definition, Steps, Examples, FAQs

Order of Operations is a collection of mathematical principles that specify the order in which distinct operations of an expression should be performed. The order is as follows:

• Parentheses First
• Then Exponents
• Then Multiplication and Division (from left to right)
• Lastly Addition and Subtraction

In this article, we will learn about the order of operation, BODMAS rule, PEDMAS rule, examples and others in detail.

What is Order of Operations?

Order of Operations is a collection of mathematical principles that determine the order in which computations are executed in an expression. These guidelines guarantee that everyone gets the same solution while solving a problem.

The order of operations and rules are expressed here:

• Brackets ( ), { }, [ ]
• Exponents
• Division (÷) and Multiplication (×)
• Addition (+) and Subtraction (-)

To calculate 5 + 3 × 2, multiply 3 by 2 to obtain 6, and then add 5 to get 11. Order of Operations is shown in the image added below,

Define Order of Operations

Order of Operations is a collection of principles used in mathematics to determine which computations to do first in an equation. Parentheses come first, followed by exponents, multiplication and division (from left to right), and addition and subtraction.

Basic Operations in Mathematics

Basic operations in mathematics are fundamental mathematical procedures that are utilised to calculate. They encompass the operations of addition, subtraction, multiplication, and division. Addition is the process of adding numbers to obtain a total or amount. Subtraction is the process of subtracting one integer from another to discover the difference. Multiplication is the process of adding multiple groups of numbers together.

Division is the reverse of multiplication, in which a number is divided into equal pieces. These operations are utilised in a variety of activities, ranging from counting money to solving complicated equations, and serve as the foundation for mathematical problem-solving. Mastering these procedures is critical for developing mathematical abilities and comprehending more advanced arithmetic ideas.

Order of Operations Rules-PEMDAS vs BODMAS

Order of Operations principles specify the order in which mathematical equations are solved, maintaining consistency and correctness throughout calculations. These criteria are critical for preventing misunderstanding and producing accurate outcomes. They include parentheses, exponents, multiplication and division, and addition and subtraction, which are often known by acronyms like as PEMDAS or BODMAS.

PEMDAS Rule

PEMDAS is an abbreviation for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction. This rule prioritises calculations in brackets first, then exponents, multiplication and division, and finally addition and subtraction.

Order of Operations PEMDAS

Order of operation in PEDMAS are,

• P stands for Parentheses ( ), { }, [ ]
• E stands for Exponents (a^b)
• M stands for Multiplication (×)
• D stands for Division (÷)
• A stands for Addition (+)
• S stands for Subtraction (-)

Examples of PEMDAS

Let’s solve the expression (3 + 2) × 4 – 6 ÷ 2 using PEMDAS

Step 1: Inside Parentheses: (3 + 2) × 4 – 6 ÷ 2 = 5 × 4 – 6 ÷ 2

Step 2: Multiplication: 5 × 4 – 6 ÷ 2 = 20 – 6 ÷ 2

Step 3: Division: 20 – 6 ÷ 2 = 20 – 3

Step 4: Subtraction: 20 – 3 = 17

So, the result is 17

BODMAS Rule

BODMAS is an abbreviation for brackets, orders (or exponents), division and multiplication (from left to right), and addition and subtraction (from left to right). BODMAS, like PEMDAS, emphasises the significance of prioritising computations within brackets or brackets first, followed by exponents, division and multiplication, and lastly addition and subtraction. BODMAS provides consistency and precision in mathematical computations.

Order of Operations BODMAS

Order of operation in BODMAS are,

• B stands for Brackets ( ), { }, [ ]
• O stands for Order
• D stands for Division (÷)
• M stands for Multiplication (×)
• A stands for Addition (+)
• S stands for Subtraction (-)

Examples of BODMAS

Let’s solve the expression 6 + 3 × 2 – 4 ÷ 2 using BODMAS

Step 1: Multiplication: 6 + 3 × 2 – 4 ÷ 2 = 6 + 6 – 4 ÷ 2

Step 2: Division: 6 + 6 – 4 ÷ 2 = 6 + 6 – 2

Step 3: Addition: 6 + 6 – 2 = 12 – 2

Step 4: Subtraction: 12 – 2 = 10

So, the result is 10

Differences Between PEMDAS and BODMAS

Following table compares PEMDAS with BODMAS

PEMDAS	BODMAS
Used for the systematic simplification of mathematical operations such as division, multiplication, addition, and subtraction.	It is also used to simplify arithmetic operations like division, multiplication, addition, and subtraction in an orderly fashion.
P = Parenthesis E = Exponents M = Multiplication D = Division A = Addition S = Subtraction	B = Brackets O = Orders D = Division M = Multiplication A = Addition S = Subtraction
Example: 5 + 3 × (4 – 2)2	Example: 8 – 2 × (4 ÷ 2)2

How to Use Order of Operations?

To utilise the Order of Operations, go in the following order: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction. Begin with completing operations within brackets, then assess exponents, multiplication and division, and ultimately addition and subtraction.

Order of Operations with Parentheses

First, solve any calculations in brackets. The remainder of the phrase should then be evaluated in accordance with the Order of Operations.

Example: Simplify 2 × (3+4)

Step 1: Solve inside the parentheses: 2 × (3+4) = 2 × 7

Step 2: Multiply: 2 × 7 = 14

Following the Order of Operations, the equation equals 14

Order of Operations with Exponents

After the brackets, address any exponents or powers in the phrase. Compute these before proceeding to the remaining operations.

Example: Simplify 2³ × 4

Step 1: Evaluate the exponent: 2³ × 4 = 8 x 4

Step 2: Multiply: 8 x 4 = 32

Following the Order of Operations, the equation equals 32

Order of Operations with Multiplication or Division and Addition or Subtraction

After working with parentheses and exponents, execute multiplication and division from left to right, followed by addition and subtraction from left to right.

Example: Simplify 6 + 4 × 3 – 2

Step 1: Multiply: 6 + 4 × 3 – 2 = 6 + 12 − 2

Step 2: Add: 6 + 12 – 2 = 18 − 2

Step 3: Subtract: 18 – 2 = 16

Following the Order of Operations, the equation equals 16.

Applications of Order of Operations

Order of operations is a set of rules that tells you which mathematical operation to do first when solving a problem with multiple operations. These operations include addition, subtraction, multiplication, and division. Here are some easy-to-understand examples of how order of operations is used in everyday situations:

• Doing Math
• Playing Games
• Following Instructions

Conclusion on Order of Operations

In conclusion, understanding the Order of Operations is critical for doing accurate mathematical calculations. Calculations may be performed methodically and consistently by following these principles, which prioritise parentheses, exponents, multiplication and division, and addition and subtraction.

Read More,

• Arithmetic Progression
• Geometric Progression

Examples on Order of Operations

Example 1: Solve expression: 8 + (5 × 3) − 2² using PEMDAS.

Solution:

Step 1: Parentheses: 8 + (5 × 3) − 2² = 8 + (15) − 2²

Step 2: Exponents: 8 + (15) − 2² = 8 + 15 − 4

Step 3: Addition: 8 + 15 − 4 = 23 − 4

Step 4: Subtraction: 23 − 4 = 19

Therefore, the solution is 19

Example 2: Solve expression: 12 − 4 × (6 ÷ 2) + 5 using BODMAS.

Solution:

Step 1: Brackets: 12 − 4 × (6 ÷ 2) + 5 = 12 − 4 × 3 + 5

Step 2: Multiplication: 12 − 4 × 3 + 5 = 12 − 12 + 5

Step 3: Addition: 12 − 12 + 5 = 12 – 17

Step 4: Subtraction: 12 – 17 = 5

Therefore, the solution is 5

Example 3: Solve expression: 3 × (4 + 2)² − 10 using Order of operation.

Solution:

Step 1: Parentheses: 3 × (4 + 2)² − 10 = 3 × (6)² − 10

Step 2: Exponents: 3 × (6)² − 10 = 3 × 36 − 10

Step 3: Multiplication: 108 − 10

Step 4: Subtraction: 98

Therefore, the solution is 98

Practice Problems on Order of Operations

P1: Using PEMDAS, solve the following expression: 8 + (5 × 3) − 2.

P2: Use BODMAS to calculate the equation 12 − 4 × (6 ÷ 2) + 5.

P3: Calculate 3 × (4 + 2)² − 10 using the Order of Operations.

P4: Use PEMDAS to simplify the formula 24 ÷ (3 × 2) + 7 − 2³.

P5: Solve the problem 9 + (6 × 2) ÷ 3 − 5 using BODMAS.

P6: Calculate 5 × (3 + 2) − 4 ÷ 2 using the Order of Operations.

FAQs on Order of Operations

What is order of operationsr?

Order of Operations is a collection of rules that specify the order in which mathematical operations should be executed in an expression. It is important because it provides consistency and precision in computations, reducing misunderstanding and ensuring the same outcome for everyone.

What are PEMDAS and BODMAS, and how do they affect order of operations?

PEMDAS and BODMAS are acronyms that help you recall the order of operations:

• Parentheses/Bracket
• Exponents/Of
• Multiplication and Division (from left to right)
• Addition and Subtraction

Which are 6 steps of order of operation?

Order of operations says that operations must be done in the following order:

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

What is BEDMAS stand for?

BEDMAS stand for Brackets, Exponents, Division, Multiplication, Addition and Subtraction.

What Operation Is Completed First In the Order of Operations?

In order of operations, we simplify parentheses or the brackets first.