Understanding and Solving Mathematical Expressions: A Comprehensive Guide

Mathematical expressions can be complex and confusing when you first encounter them. Understanding the correct order of operations is crucial to solving these expressions accurately. This article provides a detailed explanation using the BODMAS rule to solve a specific expression, along with a practical example and a step-by-step breakdown.

What is BODMAS?

The BODMAS rule is a mnemonic used to remember the order of operations in mathematics. The acronym stands for Brackets, Orders (or exponents), Division, Multiplication, Addition, and Subtraction. This rule ensures that when solving an expression, operations are performed in the correct order to arrive at the right answer.

Solving the Expression: 2×34–6×82–64[23-6]

Let's take a look at the expression 2×34–6×82–64[23-6] and solve it step-by-step using the BODMAS rule.

Step 1: Solve the Parentheses and Brackets

According to BODMAS, we first deal with operations inside the brackets or parentheses. In our expression, we need to evaluate the term [23-6]:

[23-6] [17-6] [11]

Now the expression becomes:

2×34–6×82–64[11]

Step 2: Continue with the Remaining Operations

Now, we have the simplified expression:

2×34–6×82–64×11

Next, we perform the multiplication operations as indicated by the BODMAS rule. We start with 2×34:

2×34 68

The expression now becomes:

68–6×82–64×11

Next, we perform the second multiplication operation:

6×82 492

The expression now becomes:

68–492–64×11

Then, we perform the third multiplication operation:

64×11 704

The expression now simplifies to:

68–492–704

Step 3: Perform Subtraction

Finally, we perform the subtraction operations from left to right:

68–492 -424

Then:

-424–704 -1128

So, the final answer is:

-1128

Another Example

Let's see another example to reinforce our understanding. Consider the expression:

234-68[2–6]4[23-6]

Following the BODMAS rule, we start by solving the parentheses and brackets:

[2–6] [-4]

The expression now becomes:

234-68[-4]4[11]

Next, we perform the multiplication operations:

-68×[-4] 272

The expression now becomes:

234 272–44[11]

Next, we perform another multiplication operation:

4×11 44

The expression now becomes:

234 272–44

Finally, we perform the addition and subtraction operations:

234 272 506

Then:

506–44 462

So, the final answer is:

462

Conclusion

Understanding and applying the BODMAS rule is essential for solving mathematical expressions accurately. By following the correct order of operations, you can ensure that your calculations are precise and reliable. Whether you're a student, a professional, or someone who deals with numbers on a daily basis, knowing how to use the BODMAS rule is indispensable.

Key Takeaways

BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. Always start by solving any operations inside parentheses or brackets. Perform multiplication and division from left to right before addition and subtraction. Practicing with different expressions will enhance your understanding and accuracy.

By mastering the BODMAS rule, you'll be well-equipped to handle any mathematical expressions you encounter.