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Oct 13, 2025 by windailys.com 32 views

Solving Mathematical Expressions using Brackets, Division, Multiplication, Addition, and Subtraction (BrDMMAS)

In mathematics, the order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The most commonly used order of operations is Brackets, Division, Multiplication, Addition, and Subtraction (BrDMMAS). This article will guide you through the solution of two mathematical expressions using BrDMMAS.

Expression 4.1: ${$ \left(\frac{2}{8}\right)^2+\sqrt{\frac{2}{4}}$}$

Step 1: Evaluate the Expression Inside the Brackets

The first step is to evaluate the expression inside the brackets, which is ${\frac{2}{8}}$ . To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2.

${\frac{2}{8} = \frac{2 ÷ 2}{8 ÷ 2} = \frac{1}{4}}$

Step 2: Raise the Result to the Power of 2

Next, we need to raise the result to the power of 2.

${\left(\frac{1}{4}\right)^2 = \frac{1^2}{4^2} = \frac{1}{16}}$

Step 3: Simplify the Square Root

Now, let's simplify the square root of ${\frac{2}{4}}$ .

${\sqrt{\frac{2}{4}} = \sqrt{\frac{1}{2}}}$

Step 4: Add the Results

Finally, we add the results of the two expressions.

${\frac{1}{16} + \sqrt{\frac{1}{2}}}$

To add these two expressions, we need to find a common denominator. The common denominator of 16 and 2 is 16.

${\frac{1}{16} + \sqrt{\frac{1}{2}} = \frac{1}{16} + \frac{\sqrt{2}}{16}}$

Now, we can add the two fractions.

${\frac{1}{16} + \frac{\sqrt{2}}{16} = \frac{1 + \sqrt{2}}{16}}$

Expression 4.2: ${$ \sqrt[3]{\frac{1}{27}}$}$

Step 1: Simplify the Fraction

The first step is to simplify the fraction ${\frac{1}{27}}$ .

${\frac{1}{27} = \frac{1}{3^3}}$

Step 2: Evaluate the Cube Root

Next, we need to evaluate the cube root of ${\frac{1}{3^3}}$ .

${\sqrt[3]{\frac{1}{3^3}} = \frac{1}{3}}$

In this article, we have solved two mathematical expressions using Brackets, Division, Multiplication, Addition, and Subtraction (BrDMMAS). We have shown the step-by-step solution of each expression, highlighting the importance of following the order of operations. By applying BrDMMAS, we can simplify complex mathematical expressions and arrive at the correct solution.

Key Takeaways

Brackets, Division, Multiplication, Addition, and Subtraction (BrDMMAS) is a set of rules that dictate the order in which mathematical operations should be performed.
When solving mathematical expressions, it is essential to follow the order of operations to avoid errors.
By applying BrDMMAS, we can simplify complex mathematical expressions and arrive at the correct solution.

Expression 4.1: ${\frac{1 + \sqrt{2}}{16}}$

Expression 4.2: ${\frac{1}{3}}$
Frequently Asked Questions (FAQs) about Brackets, Division, Multiplication, Addition, and Subtraction (BrDMMAS)

In our previous article, we explored the concept of Brackets, Division, Multiplication, Addition, and Subtraction (BrDMMAS) and its application in solving mathematical expressions. However, we understand that there may be many questions and doubts that readers may have. In this article, we will address some of the most frequently asked questions about BrDMMAS.

Q: What is the order of operations in BrDMMAS?

A: The order of operations in BrDMMAS is as follows:

Brackets: Evaluate expressions inside brackets first.
Division: Perform division operations next.
Multiplication: Perform multiplication operations after division.
Addition: Perform addition operations after multiplication.
Subtraction: Perform subtraction operations last.

Q: Why is it essential to follow the order of operations in BrDMMAS?

A: Following the order of operations in BrDMMAS is crucial to avoid errors and ensure that mathematical expressions are evaluated correctly. If the order of operations is not followed, it can lead to incorrect results and confusion.

Q: Can I use BrDMMAS for all types of mathematical expressions?

A: While BrDMMAS is a widely used order of operations, it may not be applicable to all types of mathematical expressions. For example, in some cases, the order of operations may be specified by the context or the problem itself. In such cases, it is essential to follow the specified order of operations.

Q: How do I apply BrDMMAS to expressions with multiple operations?

A: To apply BrDMMAS to expressions with multiple operations, follow these steps:

Identify the brackets: Identify the expressions inside brackets and evaluate them first.
Perform division and multiplication: Perform division and multiplication operations from left to right.
Perform addition and subtraction: Perform addition and subtraction operations from left to right.

Q: Can I use BrDMMAS for expressions with exponents?

A: Yes, you can use BrDMMAS for expressions with exponents. When evaluating expressions with exponents, follow the order of operations as usual, and then evaluate the exponent.

Q: What are some common mistakes to avoid when using BrDMMAS?

A: Some common mistakes to avoid when using BrDMMAS include:

Not following the order of operations: Failing to follow the order of operations can lead to incorrect results.
Not evaluating expressions inside brackets first: Failing to evaluate expressions inside brackets first can lead to incorrect results.
Not performing division and multiplication from left to right: Failing to perform division and multiplication from left to right can lead to incorrect results.

In this article, we have addressed some of the most frequently asked questions about Brackets, Division, Multiplication, Addition, and Subtraction (BrDMMAS). We hope that this article has provided valuable insights and helped to clarify any doubts that readers may have had. By following the order of operations in BrDMMAS, you can ensure that mathematical expressions are evaluated correctly and avoid common mistakes.

Key Takeaways

Brackets, Division, Multiplication, Addition, and Subtraction (BrDMMAS) is a widely used order of operations.
Following the order of operations in BrDMMAS is essential to avoid errors and ensure that mathematical expressions are evaluated correctly.
BrDMMAS can be applied to expressions with multiple operations, exponents, and other mathematical concepts.

By following the order of operations in BrDMMAS, you can ensure that mathematical expressions are evaluated correctly and avoid common mistakes. Remember to:

Evaluate expressions inside brackets first.
Perform division and multiplication from left to right.
Perform addition and subtraction from left to right.
Follow the specified order of operations when applicable.

By following these steps, you can master the art of BrDMMAS and become proficient in solving mathematical expressions.