Simplifying Math Expressions A BODMAS Rule Guide

Jul 11, 2025 by ADMIN 49 views

Simplifying Expressions with BODMAS A Comprehensive Guide

In the realm of mathematics, simplifying expressions is a fundamental skill. To ensure accuracy and consistency, we follow a specific order of operations. This order is commonly remembered by the acronym BODMAS, which stands for Brackets, Orders (powers and square roots, etc.), Division and Multiplication, Addition and Subtraction. In this comprehensive guide, we will delve into the application of BODMAS through a series of examples, ensuring a clear understanding of each step involved.

Understanding BODMAS

BODMAS serves as a roadmap for solving mathematical expressions, ensuring that we perform operations in the correct sequence. It's important to adhere to this order to arrive at the accurate answer. Let's break down what each letter signifies:

B - Brackets: Operations enclosed within brackets are always performed first. This includes parentheses (), curly braces {}, and square brackets [].
O - Orders: This refers to powers, square roots, cube roots, etc. These operations are performed after brackets.
D - Division: Division operations are performed before multiplication.
M - Multiplication: Multiplication operations come after division.
A - Addition: Addition operations are performed before subtraction.
S - Subtraction: Subtraction is the last operation to be carried out.

By following this order, we can systematically simplify complex expressions and arrive at the correct solution. Let's illustrate this with several examples.

Applying BODMAS: Step-by-Step Examples

Example A: 16 + (12 x 5)

To simplify the expression 16 + (12 x 5) using the BODMAS rule, we must first address the operation within the parentheses. Brackets take precedence in our order of operations, ensuring we handle them before any other calculations. Inside the parentheses, we have 12 x 5, which represents the multiplication of 12 and 5. Performing this multiplication gives us 60. So, the expression within the parentheses simplifies to 60. Now, our expression looks like this: 16 + 60. The next step, according to BODMAS, is to perform any addition or subtraction operations. In this case, we have the addition of 16 and 60. Adding these two numbers together, 16 + 60, results in 76. Therefore, the simplified value of the entire expression 16 + (12 x 5) is 76. This step-by-step approach ensures that we adhere strictly to the BODMAS rule, leading to accurate simplification of mathematical expressions.

Example B: (6 + 14) x 15

In the expression (6 + 14) x 15, the BODMAS rule dictates that we first address the operation enclosed within the parentheses. The parentheses contain the expression 6 + 14, which is an addition operation. When we add 6 and 14, we get 20. So, the expression inside the parentheses simplifies to 20. Now, our entire expression transforms to 20 x 15. According to BODMAS, multiplication comes after dealing with brackets. Thus, we need to perform the multiplication of 20 by 15. When we multiply 20 and 15, the result is 300. Therefore, the final simplified value of the expression (6 + 14) x 15 is 300. This careful adherence to the BODMAS rule ensures we perform the operations in the correct order, leading to the accurate simplification of the given mathematical expression.

Example C: 23 + (16 + 18)

To simplify the expression 23 + (16 + 18) following the BODMAS rule, we first focus on the operation within the parentheses. The parentheses contain the expression 16 + 18, which involves addition. By adding 16 and 18 together, we obtain a sum of 34. Thus, the expression inside the parentheses simplifies to 34. Now, our expression looks like this: 23 + 34. According to BODMAS, addition should be performed after dealing with any brackets. Therefore, we add 23 and 34. The sum of 23 and 34 is 57. So, the simplified value of the entire expression 23 + (16 + 18) is 57. This systematic approach, guided by the BODMAS rule, ensures that we execute the operations in the correct order, resulting in the accurate simplification of the expression.

Example D: (110 - 13) + 103

In simplifying the expression (110 - 13) + 103 using the BODMAS rule, we start by addressing the operation enclosed within the parentheses. Inside the parentheses, we have the subtraction 110 - 13. Performing this subtraction, we find that 110 minus 13 equals 97. Thus, the expression within the parentheses simplifies to 97. Now, our expression becomes 97 + 103. According to BODMAS, we handle addition after resolving brackets. So, we add 97 and 103. The sum of 97 and 103 is 200. Therefore, the simplified value of the entire expression (110 - 13) + 103 is 200. By diligently following the BODMAS rule, we ensure that the operations are performed in the correct sequence, leading to the accurate simplification of the expression.

Example E: 48 - (13 + 7)

To simplify the expression 48 - (13 + 7) using the BODMAS rule, our initial focus is on the operation contained within the parentheses. The expression inside the parentheses is 13 + 7, which is an addition operation. When we add 13 and 7, we get a sum of 20. Therefore, the expression inside the parentheses simplifies to 20. Now, our entire expression transforms to 48 - 20. Following the BODMAS rule, we perform subtraction after handling the brackets. Thus, we subtract 20 from 48. Subtracting 20 from 48 yields a result of 28. Hence, the simplified value of the expression 48 - (13 + 7) is 28. By consistently adhering to the BODMAS rule, we ensure that the mathematical operations are executed in the correct order, leading to the accurate simplification of the given expression.

Example F: (8 x 15) - 20

In simplifying the expression (8 x 15) - 20 according to the BODMAS rule, we begin by addressing the operation enclosed within the parentheses. Inside the parentheses, we have 8 x 15, which is a multiplication operation. When we multiply 8 by 15, we obtain 120. So, the expression inside the parentheses simplifies to 120. Our expression now looks like this: 120 - 20. According to BODMAS, subtraction is performed after dealing with brackets. Thus, we subtract 20 from 120. The result of subtracting 20 from 120 is 100. Therefore, the simplified value of the expression (8 x 15) - 20 is 100. By rigorously following the BODMAS rule, we ensure that the operations are carried out in the correct sequence, leading to the accurate simplification of the mathematical expression.

Example G: 30 - (112 + 14)

To simplify the expression 30 - (112 + 14) using the BODMAS rule, our first step is to address the operation within the parentheses. The parentheses contain the expression 112 + 14, which involves addition. Adding 112 and 14 together, we get a sum of 126. Therefore, the expression inside the parentheses simplifies to 126. Now, our expression becomes 30 - 126. According to BODMAS, subtraction is performed after handling brackets. So, we subtract 126 from 30. The result of subtracting 126 from 30 is -96. Thus, the simplified value of the expression 30 - (112 + 14) is -96. By meticulously following the BODMAS rule, we ensure that the mathematical operations are executed in the correct order, leading to the accurate simplification of the given expression.

Example H: (35 - 15) + 4

In simplifying the expression (35 - 15) + 4 according to the BODMAS rule, we begin by addressing the operation enclosed within the parentheses. Inside the parentheses, we have 35 - 15, which is a subtraction operation. Performing this subtraction, we find that 35 minus 15 equals 20. Thus, the expression within the parentheses simplifies to 20. Now, our expression becomes 20 + 4. According to BODMAS, addition comes after resolving brackets. So, we add 20 and 4. The sum of 20 and 4 is 24. Therefore, the simplified value of the entire expression (35 - 15) + 4 is 24. By diligently following the BODMAS rule, we ensure that the operations are performed in the correct sequence, leading to the accurate simplification of the expression.

Example I: 154 + (121 + 11)

To simplify the expression 154 + (121 + 11) using the BODMAS rule, we first focus on the operation within the parentheses. The parentheses contain the expression 121 + 11, which involves addition. By adding 121 and 11 together, we obtain a sum of 132. Thus, the expression inside the parentheses simplifies to 132. Now, our expression looks like this: 154 + 132. According to BODMAS, addition should be performed after dealing with any brackets. Therefore, we add 154 and 132. The sum of 154 and 132 is 286. So, the simplified value of the entire expression 154 + (121 + 11) is 286. This systematic approach, guided by the BODMAS rule, ensures that we execute the operations in the correct order, resulting in the accurate simplification of the expression.

Example J: (153 + 17) x 13

In the expression (153 + 17) x 13, the BODMAS rule dictates that we first address the operation enclosed within the parentheses. The parentheses contain the expression 153 + 17, which is an addition operation. When we add 153 and 17, we get 170. So, the expression inside the parentheses simplifies to 170. Now, our entire expression transforms to 170 x 13. According to BODMAS, multiplication comes after dealing with brackets. Thus, we need to perform the multiplication of 170 by 13. When we multiply 170 and 13, the result is 2210. Therefore, the final simplified value of the expression (153 + 17) x 13 is 2210. This careful adherence to the BODMAS rule ensures we perform the operations in the correct order, leading to the accurate simplification of the given mathematical expression.

Example K: 3 x {(5 + 3) - 3}

Simplifying the expression 3 x {(5 + 3) - 3} requires a meticulous application of the BODMAS rule, especially considering the nested brackets. We begin by focusing on the innermost brackets, which contain the expression 5 + 3. Performing this addition, we find that 5 plus 3 equals 8. So, the innermost expression simplifies to 8. Now, the expression inside the curly braces becomes {8 - 3}. We proceed to evaluate this expression. Subtracting 3 from 8 gives us 5. Thus, the expression within the curly braces simplifies to 5. Our entire expression now looks like this: 3 x 5. According to BODMAS, multiplication is the next operation to perform. Multiplying 3 by 5, we get 15. Therefore, the simplified value of the expression 3 x {(5 + 3) - 3} is 15. This step-by-step approach, guided by the BODMAS rule, ensures that we handle nested brackets correctly and arrive at the accurate simplification of the mathematical expression.

Conclusion

Mastering the BODMAS rule is crucial for simplifying mathematical expressions accurately. By following the correct order of operations, we can systematically solve even the most complex problems. Remember to prioritize brackets, orders, division and multiplication, and finally, addition and subtraction. This guide, with its detailed examples, should serve as a valuable resource in your mathematical journey. Keep practicing, and you'll become proficient in simplifying expressions with confidence.