Understanding the Mathematical Expression: 5 ÷ 5 × 55 - 5
Mathematical expressions often involve a series of operations that need to be performed in a specific order to yield the correct result. This article delves into the process of solving the expression 5 ÷ 5 × 55 - 5 step-by-step, adhering to the standard order of operations. Understanding these operations is crucial for any mathematician, student, or anyone who deals with numerical calculations.
Expression Breakdown
Let's break down the given expression: 5 ÷ 5 × 55 - 5. 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)), will guide us through the solution process.
Solving the Expression
Following the PEMDAS rule, we will solve the expression as follows:
Division and Multiplication come first. We perform these operations from left to right. Addition and Subtraction come last, also performed from left to right.Let's solve the expression step-by-step:
Step 1: Division
5 ÷ 5 1
Step 2: Multiplication
1 × 55 55
Step 3: Subtraction
55 - 5 50
Therefore, the final answer is 50.
Alternative Expressions and Solutions
Let's explore a few similar expressions for better understanding:
Expression 1:
Y5 Y5×5/55–5 Y25/55–5 Y55–5 Y10–5 Y5
Explanation:
Step 1: Division
55 ÷ 5 11
Step 2: Multiplication and Subtraction
5 × 11 - 5 55 - 5 50
Expression 2:
Z555÷5–5 Z111–5 Z106
Explanation:
Step 1: Division
555 ÷ 5 111
Step 2: Subtraction
111 - 5 106
Expression 3:
Y5 Y5/5×55–5 Y1×55–5 Y55–5 Y50
Explanation:
Step 1: Division
5 ÷ 5 1
Step 2: Multiplication and Subtraction
1 × 55 - 5 55 - 5 50
Conclusion
Understanding and applying the correct order of operations, such as PEMDAS, is essential for solving mathematical expressions accurately. Whether you're a student, a teacher, or an individual who frequently uses mathematical operations, grasping these rules will help you avoid common pitfalls and achieve the correct solutions.