Solving the Math Puzzle: 55×5÷5-5

Mathematics can sometimes be a fascinating way to explore the order of operations and how different methods lead to understanding a problem. In this article, we will delve into the solution of the math puzzle 55×5÷5-5. Whether you use the PEMDAS or BODMAS method, the result is clear and simple. Let's break it down step by step.

Understanding the Order of Operations

The order of operations is a set of rules that dictate the sequence in which operations must be performed in a mathematical expression. Two common acronyms used to remember these rules are PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)) and BODMAS (Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)). Both BODMAS and PEMDAS are equally valid and can be applied to solve this problem.

Solution Using BODMAS

Let's solve the expression 55×5÷5-5 using the BODMAS rule:

Multiplication and Division (from left to right): First, we perform multiplication and division from left to right. 55×5: Calculate the multiplication first. 55×5 275, then we have 275÷5. 275÷5 55. Addition and Subtraction (from left to right): Next, we perform addition and subtraction from left to right. 55-5 50. 50-5 45.

So, the final result using BODMAS is 50.

Solution Using PEMDAS

Now, let's solve the expression using the PEMDAS rule:

Multiplication and Division (from left to right): 55×5: Calculate the multiplication first. 55×5 275, then we have 275÷5. 275÷5 55. Addition and Subtraction (from left to right): 55-5 50. 50-5 45.

So, the final result using PEMDAS is 45.

Common Misunderstanding

It's important to note a common mistake that can lead to confusion. The expression 55×5÷5-5 is often misinterpreted as (55×5)÷5-5 or 55×(5÷5)-5. Both of these interpretations are incorrect based on the BODMAS and PEMDAS rules, which clearly indicate the order of operations must be followed as stated. The correct order of operations always dictates that multiplication and division should be done from left to right before moving on to addition and subtraction.

Conclusion

In conclusion, the solution to the puzzle 55×5÷5-5 is clearly 5. This is achieved by strictly adhering to the mathematical rules of operation, BODMAS or PEMDAS. By understanding and applying these rules, you can solve seemingly complex math problems in a straightforward manner.