BODMAS Rule: Definition, Application, and Questions

ElevatEd
Math
June 21, 2024

Math can sometimes seem hard at first. But with the right tools and understanding, it can become much easier. One important tool in arithmetic is the BODMAS rule, which helps us solve mathematical expressions in a clear and organized way. This blog will explore the BODMAS rule, covering its definition, importance, and application.

Definition of BODMAS

BODMAS is an acronym that stands for:

Brackets
Orders (i.e., powers and roots, such as squares and square roots)
Division
Multiplication
Addition
Subtraction

The BODMAS rule dictates the order in which operations should be performed in a mathematical expression to ensure accurate results. Here's a breakdown of each component:

Brackets (B): Solve expressions inside brackets first. This includes parentheses (()), square brackets ([]), and curly braces ({}).
Orders (O): Evaluate powers and roots next, such as squares (e.g., ), square roots (e.g., ), and other exponents.
Division (D) and Multiplication (M): These operations are performed from left to right. Division and multiplication are of equal precedence, so you solve them in the order they appear from left to right.
Addition (A) and Subtraction (S): These operations are also performed from left to right, following division and multiplication. Addition and subtraction are of equal precedence and are solved in the order they appear from left to right.

Importance of the BODMAS Rule

The BODMAS rule is crucial in mathematics for several reasons:

Consistency: It provides a standard procedure for solving mathematical expressions, ensuring consistency across different problems and solutions.
Accuracy: Applying the BODMAS rule helps in obtaining the correct answer by performing operations in the correct order.
Clarity: It reduces ambiguity in mathematical expressions, making them easier to understand and solve.
Foundation for Advanced Mathematics: Mastering the BODMAS rule is essential for tackling more complex mathematical concepts and operations in algebra, calculus, and beyond.

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BODMAS in Different Countries

The BODMAS rule is known by different acronyms in various countries, but the underlying principles remain the same:

PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) in the United States.
BIDMAS (Brackets, Indices, Division and Multiplication, Addition and Subtraction) in the United Kingdom.
BEDMAS (Brackets, Exponents, Division and Multiplication, Addition and Subtraction) in Canada and New Zealand.

Regardless of the acronym used, the order of operations is followed similarly to ensure accurate mathematical results.

Examples with Solutions

Example 1:
Solve 5 + 2 × ( − 1) ÷ 2

Step-by-step solution:

Brackets: 5 + 2 × (9 − 1) ÷ 2
Orders: 5 + 2 × 8 ÷ 2
Division and Multiplication: 5 + 16 ÷ 2
Division: 5 + 8
Addition: 13

So, 5 + 2 × ( − 1) ÷ 2 =13

Example 2:
Solve (4 + 6) ÷ 2 +

Step-by-step solution:

Brackets: 10 ÷ 2 +
Division and Orders: 5+9
Addition: 14

So, (4 + 6) ÷ 2 + =14

Example 3:
Evaluate 7 + [2 × ( − 4)] ÷ 5

Step-by-step solution:

Brackets: 7 + [2 × (27 − 4)] ÷ 5
Orders: 7 + [2 × 23] ÷ 5
Multiplication: 7 + 46 ÷ 5
Division: 7 + 9.2
Addition: 16.2

So, 7 + [2 × ( − 4)] ÷ 5 =16.2

Example 4:
Solve 12 ÷ 4 + (6 × ) – 3.

Step-by-step solution:

Brackets and Orders: 12 ÷ 4 + (6 × 4) – 3
Multiplication and Division: 3 + 24 – 3
Addition and Subtraction: 24

So, 12 ÷ 4 + (6 × ) – 3 = 24

Example 5:
Evaluate (15 − 3) × [ + (8 ÷ 2)]

Step-by-step solution:

Brackets and Orders: (15 − 3) × [8 + 4]
Addition: 12 × 12
Multiplication: 144

So, (15 − 3) × [ + (8 ÷ 2)] = 144

Example 6:
Calculate 30 – 12 ÷ (3 × 2) +

Step-by-step solution:

Brackets: 30 – 12 ÷ 6 + 25
Division: 30 – 2 + 25
Addition and Subtraction: 53

So, 30 – 12 ÷ (3 × 2) + = 53

Example 7:
Solve 50 ÷ [2 × ( − 1)] + 7

Step-by-step solution:

Brackets: 50 ÷ [2 × (9−1)] + 7
Orders: 50 ÷ [2 × 8] + 7
Multiplication: 50 ÷ 16 + 7
Division: 3.125+7
Addition: 10.125

So, 50 ÷ [2 × ( − 1)] + 7 = 10.125

The BODMAS rule is a fundamental concept in mathematics that ensures accuracy and consistency in solving arithmetic expressions. By understanding and applying this rule, we can simplify complex problems and achieve correct results. Whether referred to as BODMAS, PEMDAS, BIDMAS, or BEDMAS, the order of operations remains a critical tool in the mathematician's toolkit.

FAQs (Frequently Asked Questions)

Q.1. What does BODMAS stand for?
Ans: BODMAS stands for Brackets, Orders (powers and roots), Division, Multiplication, Addition, and Subtraction, which represents the order of operations in mathematical expressions.

Q.2. Why is the BODMAS rule important?
Ans: The BODMAS rule is important because it ensures consistency, accuracy, and clarity in solving mathematical expressions by providing a standard procedure for the order of operations.

Q.3. Is the BODMAS rule used universally?
Ans: Yes, the BODMAS rule is used universally, though it may be known by different acronyms in different countries, such as PEMDAS in the United States and BIDMAS in the United Kingdom.

Q.4. How does the BODMAS rule help in solving complex problems?
Ans: The BODMAS rule helps by providing a clear order for operations, allowing you to break down and solve complex expressions step-by-step, ensuring the correct solution is reached.

Q.5. Can we use the BODMAS rule when there are no brackets?
Ans: Yes, the BODMAS rule can still be applied even when there are no brackets in the expression.

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