Simplify The Expression:$\frac{-64}{-4 \times -2}$

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently and accurately. When dealing with fractions, we often need to simplify them to make them easier to work with. In this article, we will focus on simplifying the expression −64−4×−2\frac{-64}{-4 \times -2}.

Understanding the Expression

The given expression is a fraction with a negative numerator and a negative denominator. To simplify this expression, we need to understand the rules of multiplying and dividing negative numbers. When we multiply two negative numbers, the result is a positive number. Similarly, when we divide two negative numbers, the result is a positive number.

Simplifying the Expression

To simplify the expression −64−4×−2\frac{-64}{-4 \times -2}, we need to follow the order of operations (PEMDAS). First, we need to multiply the two negative numbers in the denominator.

Multiplying Negative Numbers

When we multiply two negative numbers, the result is a positive number. In this case, we have:

−4×−2=8-4 \times -2 = 8

So, the expression becomes:

−648\frac{-64}{8}

Dividing Negative Numbers

Now that we have simplified the denominator, we can divide the numerator by the denominator.

Dividing Negative Numbers

When we divide two negative numbers, the result is a positive number. In this case, we have:

−648=−8\frac{-64}{8} = -8

Therefore, the simplified expression is:

−8-8

Conclusion

In this article, we simplified the expression −64−4×−2\frac{-64}{-4 \times -2} by following the order of operations and understanding the rules of multiplying and dividing negative numbers. We learned that when we multiply two negative numbers, the result is a positive number, and when we divide two negative numbers, the result is a positive number. By applying these rules, we were able to simplify the expression to its final value of −8-8.

Frequently Asked Questions

  • What is the order of operations? The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
  • What is the rule for multiplying negative numbers? When we multiply two negative numbers, the result is a positive number.
  • What is the rule for dividing negative numbers? When we divide two negative numbers, the result is a positive number.

Tips and Tricks

  • When simplifying expressions, always follow the order of operations.
  • When multiplying or dividing negative numbers, remember that the result is always a positive number.
  • Practice simplifying expressions to become more comfortable with the rules of multiplying and dividing negative numbers.

Real-World Applications

Simplifying expressions is an essential skill in mathematics that has many real-world applications. Here are a few examples:

  • In finance, simplifying expressions can help us calculate interest rates and investment returns.
  • In science, simplifying expressions can help us calculate distances and velocities.
  • In engineering, simplifying expressions can help us design and build complex systems.

Final Thoughts

Simplifying expressions is a crucial skill in mathematics that helps us solve problems efficiently and accurately. By following the order of operations and understanding the rules of multiplying and dividing negative numbers, we can simplify even the most complex expressions. Remember to practice simplifying expressions to become more comfortable with the rules and to apply them to real-world problems.

Introduction

In our previous article, we simplified the expression −64−4×−2\frac{-64}{-4 \times -2} by following the order of operations and understanding the rules of multiplying and dividing negative numbers. In this article, we will answer some frequently asked questions related to simplifying expressions and provide additional tips and tricks to help you become more comfortable with the rules.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Q: What is the rule for multiplying negative numbers?

A: When we multiply two negative numbers, the result is a positive number.

Q: What is the rule for dividing negative numbers?

A: When we divide two negative numbers, the result is a positive number.

Q: How do I simplify an expression with multiple operations?

A: To simplify an expression with multiple operations, follow the order of operations. First, evaluate any expressions inside parentheses. Next, evaluate any exponents. Finally, perform any multiplication and division operations from left to right, and then perform any addition and subtraction operations from left to right.

Q: What is the difference between simplifying an expression and solving an equation?

A: Simplifying an expression involves reducing it to its simplest form, while solving an equation involves finding the value of the variable that makes the equation true.

Q: Can I simplify an expression with a variable?

A: Yes, you can simplify an expression with a variable. However, you will need to follow the order of operations and use the rules for multiplying and dividing negative numbers.

Q: How do I know when to simplify an expression?

A: You should simplify an expression whenever it is necessary to make the expression easier to work with. This can be the case when you are solving an equation, graphing a function, or performing other mathematical operations.

Tips and Tricks

  • Always follow the order of operations when simplifying an expression.
  • Use the rules for multiplying and dividing negative numbers to simplify expressions.
  • Practice simplifying expressions to become more comfortable with the rules.
  • Use a calculator or computer program to check your work and ensure that your simplified expression is correct.

Real-World Applications

Simplifying expressions is an essential skill in mathematics that has many real-world applications. Here are a few examples:

  • In finance, simplifying expressions can help us calculate interest rates and investment returns.
  • In science, simplifying expressions can help us calculate distances and velocities.
  • In engineering, simplifying expressions can help us design and build complex systems.

Final Thoughts

Simplifying expressions is a crucial skill in mathematics that helps us solve problems efficiently and accurately. By following the order of operations and understanding the rules of multiplying and dividing negative numbers, we can simplify even the most complex expressions. Remember to practice simplifying expressions to become more comfortable with the rules and to apply them to real-world problems.

Additional Resources

  • Khan Academy: Simplifying Expressions
  • Mathway: Simplifying Expressions
  • Wolfram Alpha: Simplifying Expressions

Conclusion

In this article, we answered some frequently asked questions related to simplifying expressions and provided additional tips and tricks to help you become more comfortable with the rules. We also discussed the importance of simplifying expressions in real-world applications and provided some additional resources for further learning. Remember to practice simplifying expressions to become more confident in your ability to solve mathematical problems.