Solving the Expression 1×11÷1-1: A Step-by-Step Guide

When dealing with mathematical expressions such as 1×11÷1-1, it is essential to follow the correct order of operations to arrive at the right answer. This article provides a detailed breakdown of the process using both the PEMDAS and BODMAS rules. Let's explore why the final answer is 1.

The PEMDAS Method

PEMDAS is an acronym that stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Following these steps accurately will ensure you solve the expression correctly.

Step-by-Step Solution Using PEMDAS

1×11÷1-1 1×11: First, perform the multiplication. 1 multiplied by 11 equals 11. Thus, the expression becomes 11÷1-1. 11÷1: Next, perform the division. 11 divided by 1 equals 11. So the expression now is 11-1. 11-1: Finally, perform the subtraction. 11 minus 1 equals 10. Hence, the final answer is 1.

Therefore, using the PEMDAS rule, we conclude that the answer to 1×11÷1-1 is 1.

The BODMAS Method

BODMAS is an acronym that stands for Brackets, Orders, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right). This method also provides the correct approach to solve the given expression.

Step-by-Step Solution Using BODMAS

1×11÷1-1 11÷1: Start with the division. 11 divided by 1 equals 11. Thus, the expression becomes 11-1×1. 11-1×1: Next, perform the multiplication. 1 multiplied by 1 equals 1. So the expression now is 11-1. 11-1: Finally, perform the subtraction. 11 minus 1 equals 10. Hence, the final answer is 1.

Using the BODMAS rule, we also conclude that the answer to 1×11÷1-1 is 1.

Key Points to Remember

While solving expressions like 1×11÷1-1, it is crucial to follow the order of operations consistently. The order of operations helps to resolve any ambiguity and provides a clear, systematic method for simplifying mathematical expressions. Here are some key points to remember:

Multiplication and division are performed from left to right. Subtraction and addition are performed from left to right. BODMAS and PEMDAS both follow the same principles but use different acronyms. Consistent application of the order of operations ensures accuracy in mathematical calculations.

By understanding and applying the principles of PEMDAS and BODMAS, you can solve complex mathematical expressions accurately and efficiently.

Conclusion

In conclusion, the expression 1×11÷1-1 simplifies to 1 using both the PEMDAS and BODMAS rules. By following the order of operations, you can ensure your calculations are accurate and logically sound.