Understanding the Sequence 9-6/3: A Comprehensive Guide
The expression 9-6/3 is a common example used to illustrate the importance of the order of operations in mathematics. In this article, we will explore the steps to evaluate this expression accurately, discuss the rules of precedence, and highlight the importance of adhering to these rules for obtaining the correct result.
Introduction
The expression 9-6/3 is often used in educational contexts to demonstrate how to correctly apply the order of operations. This sequence, when calculated, evaluates to 7, as will be explained in detail below.
Step-by-Step Evaluation
Let's break down the expression 9-6/3 using the proper order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)):
Evaluate the division first: 6/3 2 Substitute the result back into the expression: 9 - 2 Perform the subtraction: 9 - 2 7This evaluation proves that the result of the expression 9-6/3 is 7. The step-by-step approach ensures that the problem is solved correctly, adhering to the mathematical rules of precedence.
Additional Numerical Expressions
It's interesting to note that expressions like 999-6-6/3 use a limited set of numbers (nines, sixes, and threes). While this expression is more complex, breaking it down using the order of operations can still yield a clear result:
Expression: 999 - 6 - 6/3
Evaluate the division first: 6/3 2 Substitute the result back into the expression: 999 - 6 - 2 Perform the subtractions from left to right: 999 - 6 993 993 - 2 991Thus, the result of the expression 999 - 6 - 6/3 is 991.
The BODMAS Rule and Its Application
The BODMAS rule, which is another mnemonic for the order of operations, stands for Brackets, Orders (powers and square roots, etc.), Division and Multiplication (left to right), Addition and Subtraction (left to right). Applying the BODMAS rule to the expression 9 - 6 - 6/3:
Evaluate the division first: 6/3 2 Substitute the result back into the expression: 9 - 6 - 2 Perform the subtractions from left to right: 9 - 6 3 3 - 2 1Therefore, the result of the expression 9 - 6 - 6/3 is 1.
Conclusion
Understanding and applying the order of operations is crucial for solving mathematical expressions accurately. Whether dealing with the simple sequence 9-6/3 or more complex expressions, following the correct steps ensures the right solution. The guidance provided by mnemonics like BODMAS or PEMDAS makes the process more straightforward and less error-prone.