{6-3×[(25×2÷5)×(32÷2×3)]+10}

by ADMIN 29 views

=====================================================

Introduction

In this article, we will delve into the world of mathematical expressions and solve a complex equation step by step. The given equation is {6-3×[(25×2÷5)×(32÷2×3)]+10}. This equation involves various mathematical operations such as multiplication, division, and subtraction. Our goal is to simplify this expression and arrive at a final value.

Understanding the Equation

Before we begin solving the equation, let's break it down and understand its components. The equation consists of several nested expressions, which can be overwhelming at first glance. However, by following the order of operations (PEMDAS), we can simplify the equation step by step.

Step 1: Evaluate the Innermost Expressions

The innermost expressions are (25×2÷5) and (32÷2×3). Let's evaluate these expressions first.

(25×2÷5)

To evaluate this expression, we need to follow the order of operations.

  • Multiply 25 and 2: 25×2 = 50
  • Divide 50 by 5: 50÷5 = 10

So, (25×2÷5) = 10.

(32÷2×3)

Now, let's evaluate the second innermost expression.

  • Divide 32 by 2: 32÷2 = 16
  • Multiply 16 by 3: 16×3 = 48

So, (32÷2×3) = 48.

Step 2: Multiply the Innermost Expressions

Now that we have evaluated the innermost expressions, let's multiply them together.

  • Multiply 10 by 48: 10×48 = 480

So, (25×2÷5)×(32÷2×3) = 480.

Step 3: Multiply 3 by the Result

Now, let's multiply 3 by the result of the previous step.

  • Multiply 3 by 480: 3×480 = 1440

So, 3×[(25×2÷5)×(32÷2×3)] = 1440.

Step 4: Subtract 1440 from 6

Now, let's subtract 1440 from 6.

  • Subtract 1440 from 6: 6-1440 = -1434

So, 6-3×[(25×2÷5)×(32÷2×3)] = -1434.

Step 5: Add 10 to the Result

Finally, let's add 10 to the result of the previous step.

  • Add 10 to -1434: -1434+10 = -1424

So, {6-3×[(25×2÷5)×(32÷2×3)]+10} = -1424.

Conclusion

In this article, we have solved a complex mathematical equation step by step. By following the order of operations and simplifying the innermost expressions, we arrived at a final value of -1424. This equation involves various mathematical operations such as multiplication, division, and subtraction, and requires careful attention to detail to arrive at the correct solution.

Key Takeaways

  • The order of operations (PEMDAS) is crucial in solving complex mathematical equations.
  • Simplifying innermost expressions can make the equation more manageable.
  • Careful attention to detail is necessary to arrive at the correct solution.

Final Answer

The final answer to the equation {6-3×[(25×2÷5)×(32÷2×3)]+10} is -1424.

=====================================

Introduction

In our previous article, we solved the complex mathematical equation {6-3×[(25×2÷5)×(32÷2×3)]+10} step by step. In this article, we will address some of the most frequently asked questions related to this equation.

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. It is essential to follow this order to ensure accurate results.

Q: Why is it necessary to simplify innermost expressions?

A: Simplifying innermost expressions is crucial in solving complex mathematical equations. By simplifying these expressions, we can make the equation more manageable and reduce the risk of errors.

Q: What is the difference between multiplication and division?

A: Multiplication and division are two fundamental arithmetic operations. Multiplication involves repeated addition, while division involves sharing or grouping. In the equation {6-3×[(25×2÷5)×(32÷2×3)]+10}, we need to perform multiplication and division operations in the correct order to arrive at the correct solution.

Q: How do I ensure accuracy when solving complex mathematical equations?

A: To ensure accuracy when solving complex mathematical equations, it is essential to:

  • Follow the order of operations (PEMDAS)
  • Simplify innermost expressions
  • Perform calculations carefully and accurately
  • Double-check your work for errors

Q: What is the final answer to the equation {6-3×[(25×2÷5)×(32÷2×3)]+10}?

A: The final answer to the equation {6-3×[(25×2÷5)×(32÷2×3)]+10} is -1424.

Q: Can I use a calculator to solve this equation?

A: While it is possible to use a calculator to solve this equation, it is not recommended. Calculators can be prone to errors, and it is essential to understand the underlying mathematical concepts to arrive at the correct solution.

Q: How can I apply the concepts learned from this equation to real-life situations?

A: The concepts learned from this equation can be applied to various real-life situations, such as:

  • Financial calculations
  • Scientific research
  • Engineering applications
  • Data analysis

By understanding the order of operations, simplifying innermost expressions, and performing calculations accurately, you can apply these concepts to a wide range of real-life situations.

Conclusion

In this article, we have addressed some of the most frequently asked questions related to the equation {6-3×[(25×2÷5)×(32÷2×3)]+10}. By following the order of operations, simplifying innermost expressions, and performing calculations accurately, you can arrive at the correct solution and apply these concepts to real-life situations.

Key Takeaways

  • The order of operations (PEMDAS) is crucial in solving complex mathematical equations.
  • Simplifying innermost expressions can make the equation more manageable.
  • Accuracy is essential when solving complex mathematical equations.
  • The concepts learned from this equation can be applied to various real-life situations.

Final Answer

The final answer to the equation {6-3×[(25×2÷5)×(32÷2×3)]+10} is -1424.