Evaluate The Expression:$0 + \frac{1}{3} - \frac{2}{3}$Determine The Values Of:A. $a = -\frac{19}{3}$B. $a = 2$C. $\theta = \frac{19}{3}$

$$

Introduction

In mathematics, evaluating expressions is a fundamental concept that involves simplifying mathematical expressions by performing operations such as addition, subtraction, multiplication, and division. In this article, we will evaluate the expression $0 + \frac{1}{3} - \frac{2}{3}$ and determine the values of $a$ and $\theta$.

Evaluating the Expression

To evaluate the expression $0 + \frac{1}{3} - \frac{2}{3}$, we need to follow the order of operations (PEMDAS):

1. Parentheses: There are no parentheses in the expression.
2. Exponents: There are no exponents in the expression.
3. Multiplication and Division: We need to perform these operations from left to right.
4. Addition and Subtraction: We need to perform these operations from left to right.

Step 1: Simplify the Expression

First, we need to simplify the expression by performing the operations from left to right.

$$0 + \frac{1}{3} - \frac{2}{3}$$

We can start by adding 0 to $\frac{1}{3}$:

$$\frac{1}{3} - \frac{2}{3}$$

Step 2: Subtract $\frac{2}{3}$ from $\frac{1}{3}$

Now, we need to subtract $\frac{2}{3}$ from $\frac{1}{3}$.

$$\frac{1}{3} - \frac{2}{3} = -\frac{1}{3}$$

Step 3: Determine the Value of $a$

Now that we have simplified the expression, we can determine the value of $a$.

$$a = -\frac{19}{3}$$

However, we need to evaluate the expression $0 + \frac{1}{3} - \frac{2}{3}$ to determine the value of $a$.

Step 4: Evaluate the Expression

Let's evaluate the expression $0 + \frac{1}{3} - \frac{2}{3}$.

$$0 + \frac{1}{3} - \frac{2}{3} = -\frac{1}{3}$$

Step 5: Determine the Value of $a$

Now that we have evaluated the expression, we can determine the value of $a$.

$$a = -\frac{1}{3}$$

Step 6: Determine the Value of $\theta$

Now that we have determined the value of $a$, we can determine the value of $\theta$.

$$\theta = \frac{19}{3}$$

However, we need to evaluate the expression $0 + \frac{1}{3} - \frac{2}{3}$ to determine the value of $\theta$.

Step 7: Evaluate the Expression

Let's evaluate the expression $0 + \frac{1}{3} - \frac{2}{3}$.

$$0 + \frac{1}{3} - \frac{2}{3} = -\frac{1}{3}$$

Step 8: Determine the Value of $\theta$

Now that we have evaluated the expression, we can determine the value of $\theta$.

$$\theta = -\frac{1}{3}$$

Conclusion

In this article, we evaluated the expression $0 + \frac{1}{3} - \frac{2}{3}$ and determined the values of $a$ and $\theta$. We found that the value of $a$ is $-\frac{1}{3}$ and the value of $\theta$ is $-\frac{1}{3}$.

Discussion

The expression $0 + \frac{1}{3} - \frac{2}{3}$ is a simple algebraic expression that involves addition and subtraction of fractions. The order of operations (PEMDAS) is used to evaluate the expression. The value of $a$ is determined by evaluating the expression, and the value of $\theta$ is determined by evaluating the expression.

Final Answer

The final answer is $\boxed{-\frac{1}{3}}$.

References

• [1] "Order of Operations" by Math Open Reference. Accessed on February 26, 2024.
• [2] "Algebraic Expressions" by Khan Academy. Accessed on February 26, 2024.

Keywords

• Evaluate the expression
• Algebraic expressions
• Order of operations
• PEMDAS
• Addition and subtraction of fractions
• Value of $a$
• Value of $\theta$
  

$$

Introduction

In our previous article, we evaluated the expression $0 + \frac{1}{3} - \frac{2}{3}$ and determined the values of $a$ and $\theta$. In this article, we will answer some frequently asked questions related to evaluating the expression.

Q1: What is the order of operations (PEMDAS)?

A1: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

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

Q2: How do I simplify the expression $0 + \frac{1}{3} - \frac{2}{3}$?

A2: To simplify the expression $0 + \frac{1}{3} - \frac{2}{3}$, we need to follow the order of operations (PEMDAS). We can start by adding 0 to $\frac{1}{3}$:

$$\frac{1}{3} - \frac{2}{3}$$

Then, we can subtract $\frac{2}{3}$ from $\frac{1}{3}$:

$$\frac{1}{3} - \frac{2}{3} = -\frac{1}{3}$$

Q3: What is the value of $a$?

A3: The value of $a$ is determined by evaluating the expression $0 + \frac{1}{3} - \frac{2}{3}$. We found that the value of $a$ is $-\frac{1}{3}$.

Q4: What is the value of $\theta$?

A4: The value of $\theta$ is determined by evaluating the expression $0 + \frac{1}{3} - \frac{2}{3}$. We found that the value of $\theta$ is $-\frac{1}{3}$.

Q5: How do I evaluate the expression $0 + \frac{1}{3} - \frac{2}{3}$ using a calculator?

A5: To evaluate the expression $0 + \frac{1}{3} - \frac{2}{3}$ using a calculator, you can follow these steps:

1. Enter the expression into the calculator: 0 + 1/3 - 2/3
2. Press the "=" button to evaluate the expression.
3. The calculator will display the result: -1/3

Q6: Can I use a different method to evaluate the expression $0 + \frac{1}{3} - \frac{2}{3}$?

A6: Yes, you can use a different method to evaluate the expression $0 + \frac{1}{3} - \frac{2}{3}$. For example, you can use a common denominator to add and subtract the fractions:

$$\frac{1}{3} - \frac{2}{3} = \frac{1}{3} - \frac{6}{9} = \frac{3}{9} - \frac{6}{9} = -\frac{3}{9} = -\frac{1}{3}$$

Q7: What is the final answer to the expression $0 + \frac{1}{3} - \frac{2}{3}$?

A7: The final answer to the expression $0 + \frac{1}{3} - \frac{2}{3}$ is $-\frac{1}{3}$.

Conclusion

In this article, we answered some frequently asked questions related to evaluating the expression $0 + \frac{1}{3} - \frac{2}{3}$. We covered topics such as the order of operations (PEMDAS), simplifying the expression, and evaluating the expression using a calculator. We also provided alternative methods for evaluating the expression.

Final Answer

The final answer is $\boxed{-\frac{1}{3}}$.

References

• [1] "Order of Operations" by Math Open Reference. Accessed on February 26, 2024.
• [2] "Algebraic Expressions" by Khan Academy. Accessed on February 26, 2024.

Keywords

• Evaluate the expression
• Algebraic expressions
• Order of operations
• PEMDAS
• Addition and subtraction of fractions
• Value of $a$
• Value of $\theta$