Solving Complex Mathematical Expressions: A Comprehensive Guide
Mathematical expressions can sometimes seem intimidating, especially when they involve complex operations. In this guide, we will walk you through the step-by-step process of solving a particular expression using the order of operations (PEMDAS/BODMAS). This guide will help you understand how to break down and solve the equation 1/5 999494/495 × 99.
Understanding Mathematical Expressions and the Order of Operations
Mathematical expressions consist of numbers, variables, and operators. The order of operations (PEMDAS/BODMAS) ensures that expressions are evaluated correctly. Here is a quick breakdown of the order of operations:
Parentheses/Brackets (P/B): Solve what is inside parentheses or brackets first. Exponents/Orders (E/O): Solve any exponents or orders (such as square roots) next. Multiplication and Division (MD): Perform multiplication and division from left to right. Addition and Subtraction (AS): Finally, perform addition and subtraction from left to right.Solving 1/5 999494/495 × 99
Let's break down the expression 1/5 999494/495 × 99 using the order of operations. It is crucial to follow the correct order to avoid incorrect results. Here are the steps:
Step 1: Parentheses and Multiplication First, identify and simplify the multiplication within the expression. 999494/495 × 99. Simplify the fraction: 999494/495 999494 × 1/495. Then, perform the multiplication: 999494 × 99 / 495. Simplify the division: 999494 × 99 / 495 98954206 / 495 ≈ 199838.309. Step 2: Addition Now, add 1/5 to the result obtained in Step 1. So, 1/5 199838.309. Convert 1/5 to a decimal: 1/5 0.2. Perform the addition: 0.2 199838.309 199838.509.Therefore, the solution to the expression 1/5 999494/495 × 99 is approximately 199838.509.
Alternative Solution Method
Here is an alternative method to solve the same expression:
Step 1: Simplifying the Expression First, simplify the fraction: 999494/495 999494/5. Then, multiply by 99: 999494/5 × 99 999494/5 × 99. Step 2: Further Simplification Express 999494 as a multiple of 99: 999494 99 × 99999. Substitute back into the expression: 99 × 99999/5. Perform the division: 991999/5 991999. Express 991999 as a multiple of 1000: 991999 99 × 100000 99. So, 991999 99 × 1000.Hence, the alternative solution to the expression 1/5 999494/495 × 99 is 99000.
Conclusion
Solving complex mathematical expressions can be simplified by breaking them down into smaller, manageable parts and following the correct order of operations. Whether you use the PEMDAS/BODMAS method or an alternative approach, understanding the basics of operations and manipulation is key to successful problem-solving.