Mastering the Order of Operations: Understanding and Solving [12 ÷ 10 - 6]
In the realm of mathematics, understanding the order of operations is crucial for solving complex equations. This article will guide you through the process of solving the expression [12 ÷ 10 - 6], explaining each step in detail.
Understanding the Basics of the Order of Operations
The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), ensures that mathematical expressions are evaluated consistently. Let's break down the expression [12 ÷ 10 - 6] step by step.
Solving [12 ÷ 10 - 6]
Step 1: Division
According to the order of operations, we start with the division within the expression:
Step 2: Subtraction
Once the division is complete, proceed with the subtraction:
Verification and Explanation
To further illustrate the process, let's break down the solution into smaller steps:
Step 1: Perform the division:
[12 ÷ 10 1.2]
Step 2: Perform the subtraction:
[1.2 - 6 -4.8]
The final result is -4.8. To confirm this, let's solve the expression again:
[12 ÷ 10 1.2] [1.2 - 6 -4.8]Therefore, the answer to the expression [12 ÷ 10 - 6] is -4.8.
Proving the Solution
Let's use a different approach to prove the solution. We can solve the expression [12 ÷ (10 - 6)] to see if it matches our previous result:
[10 - 6 4] [12 ÷ 4 3]Clearly, [12 ÷ (10 - 6) 3] does not match our original expression [12 ÷ 10 - 6 -4.8]. This confirms that the order of operations must be strictly followed, especially when dealing with subtraction and division operations.
Conclusion
Mastery of the order of operations is essential for solving mathematical expressions correctly. For the expression [12 ÷ 10 - 6], the correct order of operations yields a solution of -4.8. Understanding and applying these rules will help you solve more complex problems effectively.