What is the PEMDAS Rule and How Is It Used in Maths?
The concept of PEMDAS rule in Maths plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Knowing and applying the order of operations ensures you solve problems accurately and avoid mistakes during calculations.
What Is PEMDAS Rule in Maths?
The PEMDAS rule in Maths is a standard order of operations used to solve arithmetic expressions with more than one operation. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. You’ll find this concept applied in arithmetic calculations, algebraic expressions, and even in solving equations in higher classes.
Key Formula for PEMDAS Rule
Here’s the sequence you should always follow when solving mixed operation problems:
Parentheses → Exponents → Multiplication & Division (left to right) → Addition & Subtraction (left to right)
Cross-Disciplinary Usage
The PEMDAS rule in Maths is not just for solving textbook problems. It’s equally important in Physics (for equation simplification), Computer Science (in coding algorithms involving calculations), and basic logical reasoning. Many aptitude and competitive exams, including JEE and Olympiads, test your grasp of order of operations for tricky questions.
Step-by-Step Illustration of PEMDAS
- Starting Example: Simplify \( 12 - 2 \times (3 + 2^2) \)
- Another Example: Calculate \( (8 + 4) \div 2^2 - 3 \)
2. Multiply: \( 2 \times 7 = 14 \)
3. Subtract from 12: \( 12 - 14 = -2 \)
Final Answer: -2
2. Exponents: \( 2^2 = 4 \)
3. Division: \( 12 \div 4 = 3 \)
4. Subtraction: \( 3 - 3 = 0 \)
Final Answer: 0
Speed Trick or Vedic Shortcut
A quick memory trick for the PEMDAS order is: Please Excuse My Dear Aunt Sally. Each initial matches the operation to follow. This makes the sequence easy to recall even in high-pressure exams. For long expressions, underline or highlight each operation as you go to avoid skipping a step—a habit taught in Vedantu’s live classes.
Try These Yourself
- Simplify: \( 5 + 2 \times 3 \)
Apply PEMDAS: Multiply first (2 × 3 = 6), then Add (5 + 6 = 11).
Final Answer: 11 - Find the result of \( 18 \div (8 - 2 \times 3) \)
- If \( x = 2 \), evaluate \( (x^2 + 4) \div 2 \times 3 \)
- Spot the mistake in solving \( 9 - 3 + 2 \times 2^2 \)
Frequent Errors and Misunderstandings
- Solving left to right for all operations (ignoring the PEMDAS hierarchy).
- Forgetting to solve exponents before multiplication or division.
- Thinking addition always comes before subtraction, when both should be solved left to right.
- Ignoring operations inside parentheses or brackets.
Relation to Other Concepts
The PEMDAS rule in Maths is closely related to concepts like BODMAS Rule (used in other countries), Order of Operations, and Arithmetic Operations. Mastering PEMDAS helps in simplifying, factorizing, and solving complex equations efficiently.
Classroom Tip
A helpful classroom tip is to use color-coding or arrows to mark each operation while solving. Visual charts of the PEMDAS sequence keep steps clear even during quick revisions. Vedantu’s Maths teachers use many mnemonic tricks and visual strategies like this for easier learning.
We explored PEMDAS rule in Maths—from its definition, formula, solved examples, common mistakes, and connections to other maths topics. Keep practicing and using the PEMDAS rule in your own homework or exams. Vedantu’s learning platform provides interactive worksheets and quizzes for extra practice, ensuring you master the order of operations with confidence!
See more about:
BODMAS Rule |
Order of Operations |
Arithmetic Operations |
Multiplying Fractions
FAQs on PEMDAS Rule in Maths: Meaning, Steps & Examples
1. What is the PEMDAS rule in Maths?
The PEMDAS rule, also known as the order of operations, dictates the sequence for solving mathematical expressions with multiple operations. It stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Following this order ensures a consistent and accurate result.
2. Are PEMDAS and BODMAS the same?
PEMDAS and BODMAS are essentially the same. They both describe the order of operations. The difference lies in the terminology: PEMDAS uses Parentheses, Exponents, Multiplication, Division, Addition, Subtraction, while BODMAS uses Brackets, Orders, Division, Multiplication, Addition, Subtraction. Both acronyms represent the identical mathematical principle.
3. How do you use the PEMDAS rule?
To use PEMDAS:
1. Solve expressions within Parentheses first.
2. Evaluate Exponents.
3. Perform Multiplication and Division from left to right.
4. Finally, perform Addition and Subtraction from left to right.
4. What is an example of a PEMDAS question?
Here's an example: 10 + 5 × 2 – 4 ÷ 2. Using PEMDAS:
1. Multiplication: 5 × 2 = 10
2. Division: 4 ÷ 2 = 2
3. Addition: 10 + 10 = 20
4. Subtraction: 20 – 2 = 18. Therefore, the answer is 18.
5. Is PEMDAS always correct for all problems?
Yes, PEMDAS provides the correct order of operations for standard arithmetic expressions. It ensures a unique and universally accepted solution. However, remember to always work from left to right when performing multiplication and division, and also when performing addition and subtraction if they appear consecutively.
6. Can PEMDAS be applied to algebraic expressions with fractions or decimals?
Yes, the PEMDAS rule applies equally to expressions involving fractions and decimals. Treat fractions and decimals as numbers and follow the order of operations as usual. For instance, 2.5 + (3/4) * 2 - 1 would be solved by the PEMDAS method in the same manner as whole numbers.
7. Does PEMDAS work differently with negative numbers or brackets inside exponents?
PEMDAS works consistently even with negative numbers and nested exponents. Remember that the exponent applies only to the base immediately preceding it. For example, in -3², the exponent applies only to 3 (resulting in -9). However, in (-3)², the exponent applies to -3 resulting in 9.
8. What happens if you ignore the PEMDAS order—how does it affect your answer?
Ignoring the PEMDAS order will likely result in an incorrect answer. The order of operations ensures a single, correct solution. Different order will lead to different, and likely wrong, answers.
9. Are there any exceptions to PEMDAS in competitive exams?
No, there are no exceptions to PEMDAS in standard mathematical problems across competitive exams. It's a fundamental rule that is always followed.
10. Can I use PEMDAS for ratios, proportions, or word problems?
While PEMDAS doesn't directly solve ratios, proportions, or word problems, it's crucial for correctly calculating parts of them. You'll use PEMDAS to solve any arithmetic within the larger problem solving approach.
11. How does PEMDAS handle expressions with only addition and subtraction (or multiplication and division)?
When an expression contains only addition and subtraction (or only multiplication and division), perform the operations from left to right. For example, 10 - 5 + 2 is solved as (10 - 5) + 2 = 7. Similarly, 6 ÷ 2 × 3 is solved as (6 ÷ 2) × 3 = 9.
12. What are some common mistakes students make when using PEMDAS?
Common mistakes include:
• Incorrectly prioritizing operations (doing addition before multiplication, for example).
• Forgetting to work from left to right when performing multiplication/division or addition/subtraction.
• Misinterpreting nested parentheses.
