How to Use PEMDAS/BODMAS to Solve Expressions Correctly
The Evaluating Order Of Operations is a fundamental concept in maths that makes sure mathematical expressions with more than one operation are solved correctly and consistently. Whether you’re preparing for exams, doing homework, or simply solving daily math problems, understanding the rules of order of operations is essential. At Vedantu, we break down complex maths topics into simple, practical steps so every student can succeed.
What is the Order of Operations?
The order of operations refers to the sequence in which operations like brackets/parentheses, exponents, multiplication, division, addition, and subtraction should be performed in a mathematical expression. If these steps are not followed, you may end up with incorrect answers. To standardize this process worldwide, acronyms like PEMDAS or BODMAS are used. These are critical for all school and competitive exams, and they help avoid confusion when solving arithmetic or algebraic expressions.
- PEMDAS stands for: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
- BODMAS stands for: Brackets, Orders, Division, Multiplication, Addition, Subtraction.
For example, in the question 8 + 12 × 2: If you solve left to right, you might calculate (8 + 12) × 2 = 20 × 2 = 40. But with the correct order, you do 12 × 2 = 24 first, then 8 + 24 = 32.
Order of Operations Rules: PEMDAS and BODMAS
These acronyms help you remember the priority for each operation:
| PEMDAS | BODMAS |
|---|---|
|
|
Multiplication and Division are of equal priority; do them from left to right. The same applies to Addition and Subtraction.
Step-by-Step Procedure for Evaluating Expressions
- Solve expressions inside Brackets/Parentheses first.
- Calculate Exponents or Orders next (like squares or square roots).
- Do all Multiplication and Division, proceeding left to right.
- Finish with Addition and Subtraction, again from left to right.
This approach ensures every part of a complex arithmetic or algebraic expression is handled in the right sequence.
Worked Examples
Let’s apply the rules through some examples:
-
Example 1: Solve 6 + 2 × 3
- Step 1: Multiplication first (2 × 3 = 6)
- Step 2: Addition 6 + 6 = 12
Final answer: 12
-
Example 2: Solve 8 + [4 × (6 - 2)²]
- Step 1: Parentheses: (6 - 2) = 4
- Step 2: Exponent: 4² = 16
- Step 3: Multiplication: 4 × 16 = 64
- Step 4: Addition: 8 + 64 = 72
Final answer: 72
-
Example 3: Evaluate 24 ÷ 4 × 2
- Left to right:
- Step 1: Division 24 ÷ 4 = 6
- Step 2: Multiplication 6 × 2 = 12
Final answer: 12
-
Example 4: Solve [2 + 3 × (4² - 1)]
- Step 1: Inside parentheses: 4² = 16; 16 - 1 = 15
- Step 2: Multiplication: 3 × 15 = 45
- Step 3: Addition: 2 + 45 = 47
Final answer: 47
Practice Problems
- Simplify 5 + 18 ÷ 3 × 2
- Evaluate (7 + 3) × 2²
- Solve 12 - 2 × (8 - 3)
- Find the value of 6 × [2 + (3 × 2)]
- Calculate 36 ÷ 3 - 2²
Try solving these using PEMDAS/BODMAS rules. (Check your answers at the end for self-assessment!)
Common Mistakes to Avoid
- Doing addition or subtraction before multiplication/division.
- Forgetting to process brackets/parentheses first.
- Not following left-to-right for multiplication/division or addition/subtraction when both are present.
- Ignoring exponents (orders) or solving them after multiplication.
- Rushing through without double-checking each step.
Real-World Applications
Order of operations appears everywhere in daily life and advanced fields. For instance, when using a calculator, entering the wrong sequence gives the wrong total; in coding and computer algorithms, correct mathematical precedence avoids costly errors. Even splitting bills or calculating discounts uses these rules. At Vedantu, we show how mastering these basics supports not just maths exams but also smart, error-free living!
In this topic, you learned how crucial the Evaluating Order Of Operations is for solving mathematical expressions accurately. By following PEMDAS/BODMAS, you can avoid mistakes, speed up problem-solving, and strengthen your foundation for both school assessments and real-life applications. Keep practicing these steps for more confidence in maths. For more on this topic, check out our Order of Operations and BODMAS Rules articles, or explore topics like Evaluating Expressions and Laws of Exponents at Vedantu.
FAQs on Evaluating Order of Operations: Step-by-Step Guide
1. What is the correct order of operations in maths?
The order of operations, often remembered by the acronyms PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction), dictates the sequence for solving mathematical expressions. It ensures consistent results.
- Parentheses/Brackets (solve expressions within parentheses first)
- Exponents/Orders (calculate exponents or powers)
- Multiplication and Division (perform these operations from left to right)
- Addition and Subtraction (perform these operations from left to right)
2. Why do we use PEMDAS or BODMAS rules?
PEMDAS/BODMAS ensures everyone solves mathematical expressions the same way, preventing ambiguity and guaranteeing the correct answer. This is crucial for consistency in mathematics and its applications.
3. Are PEMDAS and BODMAS the same?
PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) and BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) represent the same order of operations, but use different terminology. PEMDAS is common in the US, while BODMAS is used in the UK and India.
4. What is the most common mistake when evaluating expressions?
A frequent error is neglecting the left-to-right rule for multiplication/division or addition/subtraction. Remember, operations at the same level are performed sequentially from left to right.
5. How do exponents affect the order of operations?
Exponents (or powers) have higher precedence than multiplication, division, addition, and subtraction. They are evaluated after parentheses/brackets but before the other operations.
6. What is the order of operations for evaluating?
The order of operations for evaluating expressions is PEMDAS/BODMAS: Parentheses/Brackets first, then Exponents/Orders, followed by Multiplication and Division (left to right), and finally Addition and Subtraction (left to right). This systematic approach avoids errors.
7. What are the 4 steps of order of operations?
While PEMDAS/BODMAS is often presented as a mnemonic, it's more accurately described as a prioritized sequence of operations. There are several stages which include: 1. Parentheses/Brackets; 2. Exponents/Orders; 3. Multiplication & Division (left to right); 4. Addition & Subtraction (left to right).
8. Is BODMAS or PEMDAS correct?
Both BODMAS and PEMDAS are correct; they are simply different mnemonics representing the same mathematical order of operations. The order of operations is a universal rule.
9. Which are the 6 steps of order of operation?
There are not six steps in the order of operations; PEMDAS/BODMAS involves four stages: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), and Addition and Subtraction (left to right). Understanding the priority and left-to-right rule for multiplication/division and addition/subtraction is key.
10. How does the order of operations apply to scientific calculators?
Scientific calculators are programmed to follow the order of operations (PEMDAS/BODMAS). Understanding these rules ensures you input expressions correctly to obtain accurate results. Knowing the order of operations helps in avoiding mistakes when using a calculator.
11. Can order of operations rules change between programming languages?
While the fundamental principle of operator precedence is consistent, some programming languages may have variations in how they handle certain operators. It is important to understand the specific rules for operator precedence in each language. Although the core concept remains the same, nuances exist.
12. Are there historical alternatives to PEMDAS/BODMAS?
Yes, older mathematical notations sometimes implied different conventions or lacked explicit rules for operator precedence. PEMDAS/BODMAS represents a standardized approach that is now globally adopted. Historically, mathematicians used various notations; the current standardized form prevents ambiguity.
