Solving 11x11÷11: The Correct Method and Order of Operations

When approaching the math problem 11x11÷11, one often encounters varying methods and results. However, understanding the correct order of operations is crucial to reaching the right answer. In this article, we'll explore the solution using both BODMAS and PEMDAS, and discuss why some alternative methods are incorrect.

A Comparison of Methods and Correct Solution

The expression 11x11÷11 can be confusing due to the common misunderstanding of the order in which operations should be performed. One frequent mistake involves performing operations from left to right without considering the hierarchical rules of arithmetic. However, the correct solution lies in adhering to the order of operations, which is represented as BODMAS (Brackets, Orders, Division/Multiplication, Addition, and Subtraction) in the UK and PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) in the US.

Using BODMAS

Let's solve the expression 11x11÷11 using the BODMAS method:

First, perform the multiplication: 11x11 121 Next, perform the division: 121÷11 11

So, the correct answer is 11.

Common Misunderstanding: Performing Operations Left to Right

Another common misconception is to solve the expression by performing operations from left to right, which leads to an incorrect answer:

11x11 121 11-12111 12111-11 -110 -11011 -99

This method disregards the correct order of operations and provides an incorrect result. It is important to note that the expression 11x11÷11 should not be interpreted as 11x(11-12111), as parentheses are not provided, and hence, the correct order of operations must be followed.

Using PEMDAS

To further clarify, let's solve the expression using the PEMDAS method:

First, perform the multiplication: 11x11 121 Next, perform the division: 121÷11 11

The result is the same as with BODMAS, confirming that the correct answer is 11.

Advanced Application: The Concept of Division as Cancellation

A more in-depth understanding of the concept involved can be seen in the following example:

Given an expression such as (frac{a×a}{a}), where (a 11), the expression simplifies according to the rules of division:

(frac{11×11}{11} frac{121}{11} 11)

This further confirms that the correct answer is 11. It demonstrates that division can be seen as a form of cancellation, reducing the complexity of the expression.

Conclusion and Further Reading

In conclusion, the correct answer to the expression 11x11÷11 is 11. Understanding the order of operations is paramount in solving such expressions accurately. If you found this explanation helpful, please upvote and follow our space GENIUS MATHEMATICS for more insightful content on math and related topics. Remember, math is not just about numbers; it’s about understanding the logic and principles behind them.