Understanding and Solving Complex Math Expressions: A Comprehensive Guide

When dealing with complex mathematical expressions, it's crucial to understand the correct order of operations to accurately solve the problem. This guide will walk you through a step-by-step approach to solving the expression 6 2 x 3 ÷ 5 - 3 4 - 1, providing you with a clear and detailed breakdown of each operation.

The Importance of the Order of Operations

The order of operations (also known as PEMDAS or BODMAS) is a set of rules that dictate the sequence in which operations should be performed. It includes the following steps:

Parentheses or Brackets Exponents or Orders Multiplication and Division (from left to right) Addition and Subtraction (from left to right)

Solving the Expression: 6 2 x 3 ÷ 5 - 3 4 - 1

Let's start by breaking down the expression and solving it step by step.

Step 1: Initial Expression

First, let's rewrite the expression clearly:

6 2 x 3 ÷ 5 - 3 4 - 1

Step 2: Parentheses or Brackets

There are no parentheses or brackets in the expression, so we can skip this step.

Step 3: Multiplication and Division (from left to right)

Next, we perform the multiplication and division operations from left to right:

6 2 x 3 ÷ 5 - 3 4 - 1

We start with 6 u22c5 2, which equals 12: 12 x 3 ÷ 5 - 3 4 - 1

Next, we perform the multiplication 12 x 3, which equals 36: 36 ÷ 5 - 3 4 - 1

Finally, we divide 36 ÷ 5, which equals 7.2: 7.2 - 3 4 - 1

Step 4: Addition and Subtraction (from left to right)

Now, we perform the addition and subtraction operations from left to right:

7.2 - 3 4 - 1

We subtract 3 from 7.2, which equals 4.2: 4.2 - 4 - 1

Next, we subtract 4 from 4.2, which equals 0.2: 0.2 - 1

Finally, we subtract 1 from 0.2, which equals -0.8: -0.8

Another Approach:

An alternative approach is to simplify the expression step by step:

6 2 x 3 ÷ 5 - 3 4 - 1

First, we simplify the multiplication and division:

8 x 3 ÷ 2 4 - 1

Next, we perform the multiplication and division from left to right:

24 ÷ 2 4 - 1

Then, we follow the order of operations for addition and subtraction:

12 - 4 - 1

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

8 - 1

7

Conclusion

By following the correct order of operations, we can accurately solve complex mathematical expressions. In this case, the expression 6 2 x 3 ÷ 5 - 3 4 - 1 evaluates to either -0.8 or 7, depending on the interpretation of operation precedence. It's essential to understand the order of operations to ensure the correct solution.

Additional Resources

For further understanding, consider exploring the following resources:

Math is Fun - Order of Operations Khan Academy - Order of Operations