Understanding the Correct Answer to 15 x 15 ÷ 15: A Step-by-Step Guide

The correct answer to the mathematical expression 15 x 15 ÷ 15 is 15. This might seem straightforward, but it's essential to understand the order of operations to ensure your calculations are accurate. In this guide, we will break down the process step-by-step, ensuring that you grasp the concept.

What is the Order of Operations?

The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed to ensure that expressions are evaluated correctly. Two popular acronyms for the order of operations are:

PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right) BODMAS: Brackets, Orders (exponents and roots, etc.), Division and Multiplication (from left to right), Addition and Subtraction (from left to right)

Step-by-Step Calculation

Let's go through the expression 15 x 15 ÷ 15 using the BODMAS rule.

Multiplication and Division (from left to right): First, we perform the multiplication: 15 x 15 225. Next, we perform the division: 225 ÷ 15 15.

The final answer is 15.

Alternative Methods

While the step-by-step approach using PEMDAS or BODMAS provides a clear and accurate answer, there are other ways to think about the problem:

Cancellation of Terms: The expression 15 x 15 ÷ 15 can be simplified by recognizing that 15 ÷ 15 1. Therefore, the expression simplifies to 15 x 1 15. Substitution: You can also solve it by breaking it down into smaller steps. First, calculate 15 ÷ 15 to get 1, then multiply by 15 to get 15.

Why Division Should be Done Before Multiplication

It's important to perform division before multiplication because the order of operations in mathematics is crucial for maintaining consistency in calculations. For example, if you perform multiplication before division, you might get a different answer. Understanding PEMDAS and BODMAS helps you avoid such errors.

FAQs

Q: Why is the order of operations important? A: The order of operations ensures that everyone arrives at the same answer when evaluating expressions, which is critical in fields like engineering, physics, and finance. Q: Can you provide another example to practice? A: Sure! Consider the expression 8 ÷ 2(2 2). Using BODMAS: 1. First, solve the brackets: 8 ÷ 2(4) 2. Then, perform the multiplication: 8 ÷ 8 3. Finally, perform the division: 1 Q: Are there any exceptions to the order of operations? A: Generally, no exceptions exist. However, in certain contexts (like programming or advanced mathematics), additional rules or conventions might apply. Always follow the standard BODMAS or PEMDAS unless specified otherwise in your problem.

Conclusion

Understanding the order of operations is crucial for accurate mathematical calculation. By following the BODMAS or PEMDAS rules, you can solve expressions like 15 x 15 ÷ 15 with confidence, arriving at the correct answer of 15. Whether you use multiplication and division first, or cancel terms, remember that the order matters!