3 4x 5

Guri Bee

less than a minute read

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20-10-2024

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3 4x 5: Unpacking the Ambiguity and Mastering the Order of Operations

The simple sequence "3 4x 5" might look innocuous, but it's a classic example of how mathematical notation can lead to confusion. This article delves into the ambiguity of this expression and provides a clear understanding of how to solve it using the fundamental concept of the order of operations.

The Question: What is the correct answer?

This is where the confusion arises. Depending on how you interpret the expression, you could arrive at two different answers:

• Interpretation 1: 3 x (4 x 5) = 60
• Interpretation 2: (3 x 4) x 5 = 60

Both interpretations seem valid, but only one is correct.

The Answer: The Order of Operations Saves the Day

To resolve this ambiguity, we need to rely on the universally accepted order of operations, often remembered by the mnemonic PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

• Multiplication before Addition: Following PEMDAS, multiplication is performed before addition. Therefore, the correct interpretation is: (3 x 4) x 5 = 60

Let's break it down:

1. Parentheses: None in this case.
2. Exponents: None in this case.
3. Multiplication: (3 x 4) = 12. Then 12 x 5 = 60
4. Addition: Not applicable in this expression.

Avoiding Ambiguity: The Power of Parentheses

To avoid any confusion, it's always best to use parentheses to explicitly define the order of operations, especially when dealing with mixed arithmetic operations.

Example:

Instead of writing "3 4x 5", write "(3 x 4) x 5" or "3 x (4 x 5)" to ensure that the desired order of operations is clear.

Conclusion

The expression "3 4x 5" highlights the importance of understanding the order of operations. By adhering to PEMDAS, we ensure consistent and accurate calculations, eliminating ambiguity and ensuring that everyone arrives at the same solution.