Understanding the Expression 11-1×1÷1: A Comprehensive Guide
The expression 11-1×1÷1 often trips up students and can be a source of confusion. However, with the right understanding of the order of operations, this problem becomes straightforward. This guide provides a step-by-step approach to solving the expression using the PEMDAS and BODMAS rules. Let’s dive in and explore the details.
Introduction to the Expression 11-1×1÷1
The expression 11-1×1÷1 is a simple arithmetic expression that requires understanding the correct order of operations to solve accurately. Students often find it challenging because the order of operations (PEMDAS or BODMAS) must be followed carefully.
PEMDAS BODMAS: Understanding the Rules
Before we solve the expression, it’s important to understand what PEMDAS and BODMAS are and how they help in solving the expression.
PEMDAS (Please Excuse My Dear Aunt Sally)
P - Parentheses E - Exponents (powers and roots, etc.) M - Multiplication D - Division A - Addition S - SubtractionPEMDAS is the order of operations that is used to solve mathematical expressions correctly. According to PEMDAS, multiplication and division have the same precedence and are performed from left to right, followed by addition and subtraction.
BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction)
B - Brackets O - Orders (powers and roots, etc.) D - Division M - Multiplication A - Addition S - SubtractionBODMAS is similar to PEMDAS but is used in some regions. Both follow the same order of operations for solving expressions.
Solving the Expression 11-1×1÷1 Using PEMDAS
Let’s solve the expression 11-1×1÷1 step-by-step using the PEMDAS rule.
Step 1: Multiplication
First, we perform the multiplication from left to right:
11-1×1÷1 11-1÷1
Step 2: Division
Next, we perform the division:
11-1÷1 11-1
Step 3: Subtraction
Finally, we perform the subtraction:
11-1 10
Thus, the value of the expression 11-1×1÷1 is 10.
Solving the Expression 11-1×1÷1 Using BODMAS
Now, let's solve the same expression using the BODMAS rule.
Step 1: Multiplication
First, we perform the multiplication from left to right:
11-1×1÷1 11-1÷1
Step 2: Division
Next, we perform the division:
11-1÷1 11-1
Step 3: Subtraction
Finally, we perform the subtraction:
11-1 10
So, the same expression 11-1×1÷1 also simplifies to 10 under the BODMAS rule.
Conclusion
Both PEMDAS and BODMAS adhere to the same principles and lead to the same result when solving the expression 11-1×1÷1. The value of the expression is 10.
FAQs
Q: Why is the expression 11-1×1÷1 10?Using the correct order of operations (PEMDAS or BODMAS), we first perform the multiplication and division from left to right, followed by subtraction. This results in the correct value of 10. Q: Can the value of 11-1×1÷1 be different if PEMDAS and BODMAS are not followed?
No, following the correct order of operations is crucial. Different orders will lead to different results, but the correct method will always yield 10. Q: What is the importance of understanding the order of operations?
The order of operations ensures consistent and accurate results in mathematical expressions. Without it, simple expressions can lead to incorrectly calculated results.