BODMAS Rule: Definition, Rules and Sample Questions

BODMAS rule is an acronym for remembering the order of operations to utilize while solving arithmetic problems. When compared to operations involving two integers, an arithmetic expression requiring numerous operations such as addition, subtraction, multiplication, and division is difficult to solve. It's simple to perform a two-number operation, but how can you solve an expression with brackets and many operations, as well as how to simplify a bracket? The BODMAS rule is designed to solve complex arithmetic operations in this scenario. B indicates brackets, O stands for the order of powers or roots, D stands for division, M stands for multiplication, A stands for addition, and S stands for subtraction. It signifies that expressions with numerous operators must be simplified in this order only, from left to right. In this article, we will understand how to apply the BODMAS rule and look at some sample questions.

Keyterms: BODMAS rule, Operations, Arithmetic problems, Complex arithmetic operations, Addition, Subtraction, Multiplication, Division

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What is the BODMAS Rule?

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To solve any arithmetic statement, you can use the BODMAS rule, i.e. first, solve the terms in brackets, then simplify exponential terms and go on to division and multiplication operations, and finally, work on addition and subtraction. Following the BODMAS rule's order of operations always yields the correct answer.

The terms within the brackets can be quickly simplified. This means that we can divide, multiply, add, and subtract in the order provided inside the brackets. If an expression contains numerous brackets, all of the same types of brackets can be solved at the same time.

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Order of Operations

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The order of operations is a set of common principles that represent standards about which process to run first to assess a given numerical statement in logic-oriented courses like mathematics. It's simple to calculate the result with a basic summation that just has two integers and one single operation, or sign. Addition, subtraction, multiplication, and division are the four operations.

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Interpretation of BODMAS Rule

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The BODMAS Rule illustrates what operations should be performed in what order when solving an expression. If an expression involves brackets ((), {}, []), we must first solve or simplify the bracket, then 'order' (that is, powers and roots, etc.), then division, multiplication, addition, and subtraction from left to right, according to the BODMAS rule. If you solve the issue in the wrong order, you'll get the wrong answer.

If the expression contains more than one operator, the BODMAS rule can be used. In this scenario, we must first simplify the words within the bracket, from the innermost to the outermost bracket [{()}], as well as any roots or exponents. Then, from left to right, conduct multiplication or division operations. Finally, use addition or subtraction to arrive at the correct solution. However one must note that the "O" in the BODMAS complete form also stands for "Order," which relates to numbers involving powers, square roots, and so on.

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Full-Form of BODMAS

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BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. The order of these procedures should be followed when applying the BODMAS rule.

This rule shows how to solve an equation in the correct order (order of precedence), and it must be followed to produce accurate answers.

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BODMAS Rule VS PEMDAS Rule

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The acronyms BODMAS and PEMDAS are used to recall the order of operations. The BODMAS rule is similar to the PEMDAS rule in many ways. Because various terms are known by different names in different nations, there is a variance in the abbreviation. When applying the BODMAS or PEMDAS rules, keep in mind that we solve the operation that occurs first from the left side of the expression when we get to the division and multiplication steps. The same rule applies to addition and subtraction: we solve the operation on the left side that appears first.

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When to use the BODMAS Rule?

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When a mathematical equation has more than one operation, BODMAS is employed. When employing the BODMAS approach, there is a set of rules that must be followed in order. This provides an appropriate structure for each mathematical expression to provide a unique solution.

Rules & Conditions

• If any brackets exist, open them and then add or remove the terms. For instance, a + (b + c) = a + b + c, a + (b - c) = a + b - c
• If a negative sign appears, simply open the bracket and multiply the negative sign with each phrase inside. For instance, a – (b + c) ⇒ a – b – c
• If there is a term just outside the bracket, multiply it by each term inside. For example, a(b + c) ⇒ ab + ac

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Easiest Method to Remember BODMAS Rule

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The following are some easy and basic principles to remember the BODMAS rule:

Step 1: First, simplify the brackets.

Step 2: Make a list of all exponential terms and solve them.

Step 3: Divide or multiply the numbers (go from left to right)

Step 4: Perform subtraction or addition (go from left to right)

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Common Mistakes while applying BODMAS Rule

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When using the BODMAS rule to simplify expressions, one can make certain typical mistakes, which are listed below:

• Multiple brackets may cause confusion, and we may receive an incorrect answer as a result. If an expression contains numerous brackets, all of the same types of brackets can be solved at the same time.
• Assuming that division takes precedence over multiplication and addition takes precedence over subtraction is a mistake. Following the left-to-right rule when selecting these procedures aids in obtaining the correct result.
• Multiplication and division are same-level operations that must be performed in the order of left to right (whatever appears first in the statement), while addition and subtraction are same-level operations that must be performed after multiplication and division. If you solve division first, then multiplication (which is on the left side of division), as D occurs before M in BODMAS, you can get the incorrect answer.
• In some circumstances, an error occurs as a result of a lack of comprehension of integer addition and subtraction. 1 - 3 + 4 = - 2 + 4 = 2, for example. However, there are situations when the following errors are made, which result in the incorrect answer, such as 1- 3 + 4 = 1 - 7 = - 6.

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Things to Remember

• Brackets, Order, Division, Multiplication, Addition, and Subtraction are abbreviated as BODMAS. This rule shows how to solve an equation in terms of the order of operations (order of precedence).
• In logic-oriented courses like mathematics, the order of operations is a set of common principles that establish guidelines for which procedure to execute first to analyze a given numerical statement.
• When a mathematical equation has more than one operation, BODMAS is employed. This provides an appropriate structure for each mathematical expression to provide a unique solution.
• According to the BODMAS rule, in a given mathematical expression containing the following signs: brackets, multiplication, of, addition, subtraction, and division, we must first solve or simplify the brackets, then of (powers and roots, etc.), of, division, multiplication, addition, subtraction, and subtraction from left to right.
• The BODMAS rule explains how to solve a mathematical expression to mathematicians. BODMAS is a critical idea that has proven to be effective in a variety of situations requiring quick calculations.

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