Solving the Equation 4 ÷ 2×3 - 13 - 5: A Comprehensive Guide

When dealing with mathematical expressions, it's important to understand the correct order of operations to obtain the right result. This article will guide you through solving the equation 4 ÷ 2×3 - 13 - 5 step by step, using the proper order of operations, and discussing why the initial solution was incorrect.

Understanding the Order of Operations

When faced with a complex expression, it's crucial to follow the correct order of operations. In mathematics, this is commonly referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)) or BODMAS (Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)).

The Correct Solution

Let's solve the equation 4 ÷ 2×3 - 13 - 5 step by step:

First, we need to perform the division and multiplication from left to right: 4 ÷ 2 2 2×3 6 Substituting these results back into the equation, we have: 6 - 13 - 5 Next, we perform the subtraction from left to right: 6 - 13 -7 -7 - 5 -12 Therefore, the correct solution is -12.

The Misleading Solution and Why It's Incorrect

Let's look at the misleading solution provided earlier and understand why it was incorrect:

The initial solution presented the expression as 4/23 - 13 - 5. Then, it divided 2 and 3, resulting in 23 - 1 - 5 6 - 10 -4. Another incorrect approach was to initially compute 4/2 2, which is correct but the next steps were misleading. The incorrect solution approached the expression in a non-standard way, leading to an incorrect result of 3, instead of the correct -12.

Importance of PEMDAS/BODMAS

The order of operations is crucial for obtaining the right result, especially with complex expressions. Here's a review of PEMDAS/BODMAS:

Parentheses/Brackets: Solve expressions within parentheses first. Exponents/Orders: Calculate any exponents or powers next. Multiplication and Division: Perform multiplication and division from left to right. Addition and Subtraction: Lastly, perform addition and subtraction from left to right.

Understanding these rules will help you solve complex equations accurately, ensuring that you don't end up with misleading or incorrect results.

Conclusion

By following the correct order of operations, you can solve the equation 4 ÷ 2×3 - 13 - 5 accurately. The correct solution is -12. Misleading solutions often arise when the order of operations is not followed correctly. Always remember to perform division and multiplication before subtraction and addition, and always work from left to right within these operations.

Further Reading

For more information and practice, consider reading this article or exploring further resources on the web related to order of operations.