PEMDAS Rule - Definition, Uses , Examples

PEMDAS Rule

Have you ever been asked to solve a math problem and get a different answer from your friend, despite doing the same question? That normally occurs when the order of operations is not taken in the proper order. In mathematics, the order in which we do operations like addition, subtraction, multiplication, and division is very important. To help everyone follow the same steps and get the same correct answer, mathematicians use the PEMDAS Rule.

PEMDAS Rule helps us know how to apply the first operation when solving mathematical expressions which contain more than one operation. It is abbreviated as Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. This simple rule keeps our math work organized and accurate. Students can learn and understand what PEMDAS is, when to use PEMDAS, examples, and more below.

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What is PEMDAS?

PEMDAS Rule is a sequence of procedures that inform us of the proper sequence of operation in a mathematical expression. PEMDAS is not a thing but an acronym, or rather, every single letter denotes one of the mathematical operations. Let’s break it down:

• P – Parentheses: Do the operations inside brackets first.

• E – Exponents: Next, solve powers or roots (like squares or square roots).

• M – Multiplication and D – Division: Then, perform multiplication and division from left to right.

• A – Addition and S – Subtraction: Finally, do addition and subtraction from left to right.

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PEMDAS Rule Definition

PEMDAS Rule In any mathematical expression that contains more than one operation, the order of operation is correct: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Example of the PEMDAS Rule:

Expression: 8 + 2 × (3² - 1)

Step-by-step solution using PEMDAS:

1. Parentheses: (3² - 1 = 9 - 1 = 8)

2. Multiplication: (2 × 8 = 16)

3. Addition: (8 + 16 = 24)

Answer: 24 If the operations are not followed in this order, the result would be incorrect. This demonstrates the importance of applying the PEMDAS Rule accurately.

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When to Use PEMDAS Rule?

PEMDAS Rule works in the case when mathematical expressions have more than one kind of operation. It helps to ensure that every operation is carried out in the right order.

1. Expressions with Multiple Operations

Expressions such as (5 + 2 × 3) include both addition and multiplication. According to PEMDAS, multiplication is performed first: (2 × 3 = 6), then addition: (5 + 6 = 11).

2. Expressions Containing Parentheses

Operations inside parentheses are always completed first. Example: 4 × (2 + 3)²

• Parentheses: (2 + 3 = 5)

• Exponent: (5² = 25)

• Multiplication: (4 × 25 = 100)

3. Expressions with Exponents

Exponents are evaluated immediately after parentheses.

• Example: (2 + 3² = 2 + 9 = 11)

4. Algebraic Expressions

In algebra, expressions such as x + 2(x - 3)² must follow the PEMDAS order to ensure accuracy. Parentheses and exponents are addressed first before performing other operations.

5. Programming and Calculator Operations.

PEMDAS is automatically followed by most modern calculators and computer programs. Parentheses have to be in the right place (or you would get the wrong results).

6. Academic Problems and Examination.

It is commonly tested in mathematical testing on understanding order of operations. PEMDAS will be used correctly to provide accurate and consistent solutions.

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PEMDAS Rule Examples

The following examples illustrate how the PEMDAS Rule is applied step by step in different mathematical situations. 

Example 1: Basic Multiplication and Addition

Question: Simplify 6 + 3 × 2 using the PEMDAS Rule.

Answer:

Step 1: Perform multiplication first → 3 × 2 = 6.
Step 2: Then add → 6 + 6 = 12.
Final Answer: 12

Example 2: Parentheses and Exponent

Question: Simplify (4 + 2)² - 5 using the PEMDAS Rule.
Answer:
Step 1: Solve inside the parentheses → 4 + 2 = 6.
Step 2: Apply the exponent → 6² = 36.
Step 3: Subtract → 36 - 5 = 31.
Final Answer: 31

Example 3: Division, Multiplication, and Parentheses

Question: Simplify 8 ÷ 2 × (2 + 2) using the PEMDAS Rule.
Answer:
Step 1: Solve parentheses → 2 + 2 = 4.
Step 2: Perform division first → 8 ÷ 2 = 4.
Step 3: Multiply → 4 × 4 = 16.
Final Answer: 16

Example 4: Exponent Inside Parentheses

Question: Simplify 5 + (3 × 2)² using the PEMDAS Rule.
Answer:
Step 1: Solve parentheses → 3 × 2 = 6.
Step 2: Apply the exponent → 6² = 36.
Step 3: Add → 5 + 36 = 41.
Final Answer: 41

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BODMAS vs PEMDAS Rule

The BODMAS and PEMDAS rules are both methods used to determine the order of operations in mathematical expressions. Though they differ slightly in terminology, they ultimately follow the same operational logic. Below is a comparison of the key differences between the two:

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