Simplify The Expression. Use The Order Of Operations. − 50 ( − 2 5 ) ÷ ( 4 ⋅ 9 − 34 -50\left(-\frac{2}{5}\right) \div (4 \cdot 9 - 34 − 50 ( − 5 2 ) ÷ ( 4 ⋅ 9 − 34 ]

Mar 10, 2025 by ADMIN 168 views

**Simplify the Expression: A Step-by-Step Guide to Using the Order of Operations**

Introduction

In mathematics, expressions can be complex and require careful evaluation to simplify them. One of the most important concepts in simplifying expressions is the order of operations, which dictates the order in which mathematical operations should be performed. In this article, we will explore how to simplify the expression $-50\left(-\frac{2}{5}\right) \div (4 \cdot 9 - 34)$ using the order of operations.

Understanding the Order of Operations

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Simplifying the Expression

Now that we have a good understanding of the order of operations, let's apply it to the given expression: $-50\left(-\frac{2}{5}\right) \div (4 \cdot 9 - 34)$ .

Step 1: Evaluate Expressions Inside Parentheses

The first step is to evaluate any expressions inside parentheses. In this case, we have two expressions inside parentheses: $-50\left(-\frac{2}{5}\right)$ and $(4 \cdot 9 - 34)$ .

-50\left(-\frac{2}{5}\right) = \frac{100}{5} = 20

(4 \cdot 9 - 34) = 36 - 34 = 2

Step 2: Evaluate Exponential Expressions

There are no exponential expressions in this problem, so we can move on to the next step.

Step 3: Evaluate Multiplication and Division Operations

Now that we have evaluated the expressions inside parentheses, we can evaluate the multiplication and division operations. In this case, we have a division operation: $20 \div 2$ .

20 \div 2 = 10

Step 4: Evaluate Addition and Subtraction Operations

There are no addition and subtraction operations in this problem, so we can move on to the final step.

Step 5: Final Answer

The final answer is $10$ .

Conclusion

Simplifying expressions using the order of operations is an essential skill in mathematics. By following the steps outlined in this article, we can simplify even the most complex expressions. Remember to always evaluate expressions inside parentheses first, followed by exponents, multiplication and division, and finally addition and subtraction. With practice and patience, you will become proficient in simplifying expressions and solving mathematical problems.

Common Mistakes to Avoid

When simplifying expressions using the order of operations, there are several common mistakes to avoid:

Not evaluating expressions inside parentheses first: This can lead to incorrect answers and confusion.
Not following the order of operations: This can also lead to incorrect answers and confusion.
Not simplifying expressions fully: This can lead to unnecessary complexity and confusion.

Real-World Applications

Simplifying expressions using the order of operations has many real-world applications, including:

Science and Engineering: Simplifying expressions is essential in science and engineering, where complex mathematical models are used to describe and analyze physical systems.
Finance: Simplifying expressions is also essential in finance, where complex mathematical models are used to analyze and manage financial risk.
Computer Science: Simplifying expressions is also essential in computer science, where complex mathematical algorithms are used to solve problems and analyze data.

Practice Problems

To practice simplifying expressions using the order of operations, try the following problems:

$3 \cdot 2 + 5 \div 2$
$10 \div 2 - 3 \cdot 2$
$4 \cdot 9 - 34 \div 2$

Additional Resources

For additional resources on simplifying expressions using the order of operations, try the following:

Math textbooks: Many math textbooks include chapters on simplifying expressions using the order of operations.
Online resources: There are many online resources available that provide step-by-step instructions and examples on simplifying expressions using the order of operations.
Math software: Many math software programs, such as Mathematica and Maple, include tools for simplifying expressions using the order of operations.
Simplify the Expression: A Q&A Guide to Using the Order of Operations ====================================================================

Introduction

In our previous article, we explored how to simplify the expression $-50\left(-\frac{2}{5}\right) \div (4 \cdot 9 - 34)$ using the order of operations. In this article, we will answer some frequently asked questions about simplifying expressions using the order of operations.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Why is it important to follow the order of operations?

A: Following the order of operations is essential to ensure that mathematical expressions are evaluated correctly. If the order of operations is not followed, the result of the expression may be incorrect.

Q: What happens if there are multiple operations with the same precedence?

A: If there are multiple operations with the same precedence, the order in which they are evaluated is determined by the order in which they appear from left to right.

Q: Can I use the order of operations to simplify expressions with fractions?

A: Yes, you can use the order of operations to simplify expressions with fractions. When simplifying expressions with fractions, it is essential to follow the order of operations and to simplify the fractions before performing any other operations.

Q: How do I simplify expressions with exponents?

A: To simplify expressions with exponents, you need to follow the order of operations and evaluate the exponents before performing any other operations. When simplifying expressions with exponents, it is essential to remember that exponents are evaluated before any other operations.

Q: Can I use the order of operations to simplify expressions with decimals?

A: Yes, you can use the order of operations to simplify expressions with decimals. When simplifying expressions with decimals, it is essential to follow the order of operations and to simplify the decimals before performing any other operations.

Q: How do I simplify expressions with negative numbers?

A: To simplify expressions with negative numbers, you need to follow the order of operations and evaluate the negative numbers before performing any other operations. When simplifying expressions with negative numbers, it is essential to remember that negative numbers are evaluated before any other operations.

Q: Can I use the order of operations to simplify expressions with variables?

A: Yes, you can use the order of operations to simplify expressions with variables. When simplifying expressions with variables, it is essential to follow the order of operations and to simplify the variables before performing any other operations.