Calculate The Following Expression: ${ 2.34 - (-5.89) }$

Introduction

Mathematical expressions can be complex and challenging to simplify, but with a clear understanding of the rules and operations involved, we can break them down into manageable parts. In this article, we will focus on calculating the expression: ${ 2.34 - (-5.89) }$. We will explore the concept of negative numbers, the order of operations, and how to simplify expressions involving subtraction and addition.

Understanding Negative Numbers

Before we dive into the expression, it's essential to understand the concept of negative numbers. A negative number is a number that is less than zero. It is denoted by a minus sign (-) preceding the number. For example, -5 is a negative number, meaning it is 5 units below zero.

The Order of Operations

When simplifying mathematical expressions, it's crucial to follow the order of operations (PEMDAS):

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

Calculating the Expression

Now that we have a solid understanding of negative numbers and the order of operations, let's focus on calculating the expression: ${ 2.34 - (-5.89) }$.

To simplify this expression, we need to follow the order of operations:

1. Evaluate the expression inside the parentheses: ${ -(-5.89) }$
2. The double negative sign indicates that we need to change the sign of the number inside the parentheses. Therefore, ${ -(-5.89) = 5.89 }$
3. Now that we have evaluated the expression inside the parentheses, we can rewrite the original expression as: ${ 2.34 - 5.89 }$
4. Finally, we can subtract 5.89 from 2.34 to get the final result.

Simplifying the Expression

To simplify the expression ${ 2.34 - 5.89 }$, we need to perform the subtraction operation.

$${ 2.34 - 5.89 = -3.55 }$$

Therefore, the final result of the expression ${ 2.34 - (-5.89) }$ is ${ -3.55 }$.

Conclusion

In this article, we have explored the concept of negative numbers and the order of operations. We have also calculated the expression ${ 2.34 - (-5.89) }$ step by step. By following the order of operations and understanding the concept of negative numbers, we can simplify complex mathematical expressions with ease.

Frequently Asked Questions

Q: What is the difference between a positive and negative number?

A: A positive number is a number that is greater than zero, while a negative number is a number that is less than zero.

Q: How do I simplify an expression involving subtraction and addition?

A: To simplify an expression involving subtraction and addition, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses, then perform any multiplication and division operations from left to right, and finally, perform any addition and subtraction operations from left to right.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The order of operations is:

1. Parentheses
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction

Q: How do I evaluate an expression with a double negative sign?

A: When evaluating an expression with a double negative sign, change the sign of the number inside the parentheses. For example, ${ -(-5.89) = 5.89 }$

Q: What is the final result of the expression ${ 2.34 - (-5.89) }$?

Q&A: Simplifying Mathematical Expressions

In this article, we will continue to explore the concept of simplifying mathematical expressions. We will answer some frequently asked questions and provide additional examples to help you understand the process.

Q: What is the difference between a positive and negative number?

A: A positive number is a number that is greater than zero, while a negative number is a number that is less than zero.

Example: 5 is a positive number, while -3 is a negative number.

Q: How do I simplify an expression involving subtraction and addition?

A: To simplify an expression involving subtraction and addition, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses, then perform any multiplication and division operations from left to right, and finally, perform any addition and subtraction operations from left to right.

Example: Simplify the expression ${ 2.34 - 5.89 + 3.45 }$

1. Evaluate any expressions inside parentheses: None
2. Perform any multiplication and division operations: None
3. Perform any addition and subtraction operations from left to right:

$${ 2.34 - 5.89 = -3.55 }$$

$${ -3.55 + 3.45 = -0.10 }$$

Therefore, the final result of the expression ${ 2.34 - 5.89 + 3.45 }$ is ${ -0.10 }$.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The order of operations is:

1. Parentheses
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction

Example: Simplify the expression ${ 2 \times 3 + 4 - 2 }$

1. Evaluate any expressions inside parentheses: None
2. Perform any multiplication and division operations from left to right:

$${ 2 \times 3 = 6 }$$

3. Perform any addition and subtraction operations from left to right:

$${ 6 + 4 = 10 }$$

$${ 10 - 2 = 8 }$$

Therefore, the final result of the expression ${ 2 \times 3 + 4 - 2 }$ is ${ 8 }$.

Q: How do I evaluate an expression with a double negative sign?

A: When evaluating an expression with a double negative sign, change the sign of the number inside the parentheses. For example, ${ -(-5.89) = 5.89 }$

Example: Simplify the expression ${ 2.34 - (-5.89) }$

1. Evaluate any expressions inside parentheses: ${ -(-5.89) = 5.89 }$
2. Perform any multiplication and division operations: None
3. Perform any addition and subtraction operations from left to right:

$${ 2.34 - 5.89 = -3.55 }$$

Therefore, the final result of the expression ${ 2.34 - (-5.89) }$ is ${ -3.55 }$.

Q: What is the final result of the expression ${ 2.34 - (-5.89) }$?

A: The final result of the expression ${ 2.34 - (-5.89) }$ is ${ -3.55 }$.

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

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

Example: Simplify the expression ${ 2 \times 3 + 4 - 2 + 1 }$

1. Evaluate any expressions inside parentheses: None
2. Perform any multiplication and division operations from left to right:

$${ 2 \times 3 = 6 }$$

3. Perform any addition and subtraction operations from left to right:

$${ 6 + 4 = 10 }$$

$${ 10 - 2 = 8 }$$

$${ 8 + 1 = 9 }$$

Therefore, the final result of the expression ${ 2 \times 3 + 4 - 2 + 1 }$ is ${ 9 }$.

Conclusion

In this article, we have answered some frequently asked questions and provided additional examples to help you understand the process of simplifying mathematical expressions. By following the order of operations and understanding the concept of negative numbers, you can simplify complex mathematical expressions with ease.

Frequently Asked Questions

Q: What is the difference between a positive and negative number?

A: A positive number is a number that is greater than zero, while a negative number is a number that is less than zero.

Q: How do I simplify an expression involving subtraction and addition?

A: To simplify an expression involving subtraction and addition, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses, then perform any multiplication and division operations from left to right, and finally, perform any addition and subtraction operations from left to right.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The order of operations is:

1. Parentheses
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction

Q: How do I evaluate an expression with a double negative sign?

A: When evaluating an expression with a double negative sign, change the sign of the number inside the parentheses. For example, ${ -(-5.89) = 5.89 }$

Q: What is the final result of the expression ${ 2.34 - (-5.89) }$?

A: The final result of the expression ${ 2.34 - (-5.89) }$ is ${ -3.55 }$.