The Difference Of A Number And 4 3 \frac{4}{3} 3 4 ​ Is 11 3 \frac{11}{3} 3 11 ​ . What Is The Number?First, Write An Equation To Describe The Situation.

Introduction

In this article, we will delve into a mathematical puzzle that involves a simple yet intriguing equation. The problem states that the difference of a number and $\frac{4}{3}$ is $\frac{11}{3}$. Our goal is to identify the unknown number that satisfies this condition. To begin, we need to write an equation that describes the situation.

Writing the Equation

Let's denote the unknown number as $x$. The problem states that the difference between this number and $\frac{4}{3}$ is $\frac{11}{3}$. Mathematically, we can represent this as:

$$x - \frac{4}{3} = \frac{11}{3}$$

This equation tells us that the unknown number $x$ minus $\frac{4}{3}$ equals $\frac{11}{3}$.

Solving the Equation

To find the value of $x$, we need to isolate it on one side of the equation. We can do this by adding $\frac{4}{3}$ to both sides of the equation. This will cancel out the $\frac{4}{3}$ on the left-hand side, leaving us with the value of $x$.

$$x - \frac{4}{3} + \frac{4}{3} = \frac{11}{3} + \frac{4}{3}$$

Simplifying the left-hand side, we get:

$$x = \frac{11}{3} + \frac{4}{3}$$

Now, let's add the fractions on the right-hand side. Since they have the same denominator, we can simply add the numerators:

$$x = \frac{11 + 4}{3}$$

$$x = \frac{15}{3}$$

Simplifying the Fraction

The fraction $\frac{15}{3}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3. This gives us:

$$x = \frac{15 \div 3}{3 \div 3}$$

$$x = \frac{5}{1}$$

$$x = 5$$

Conclusion

In this article, we have successfully unraveled the mystery of the unknown number. By writing an equation that describes the situation, we were able to isolate the value of $x$ and find that it equals 5. This demonstrates the power of algebra in solving mathematical puzzles and equations.

Real-World Applications

While this problem may seem trivial, it has real-world applications in various fields such as finance, engineering, and science. For instance, in finance, understanding the difference between two values can help investors make informed decisions about their investments. In engineering, knowing the difference between two values can be crucial in designing and building complex systems.

Tips and Tricks

When solving equations, it's essential 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 any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

By following these steps, you can ensure that you're solving equations correctly and efficiently.

Common Mistakes

When solving equations, it's easy to make mistakes. Here are some common pitfalls to avoid:

• Forgetting to simplify fractions: Make sure to simplify fractions by dividing both the numerator and the denominator by their greatest common divisor.
• Not following the order of operations: Always follow the order of operations (PEMDAS) to ensure that you're solving equations correctly.
• Not checking your work: Double-check your work to ensure that you've solved the equation correctly.

Q&A: Frequently Asked Questions

Q: What is the difference between a number and $\frac{4}{3}$? A: The difference between a number and $\frac{4}{3}$ is $\frac{11}{3}$.

Q: How do I write an equation to describe the situation? A: To write an equation, let's denote the unknown number as $x$. The problem states that the difference between this number and $\frac{4}{3}$ is $\frac{11}{3}$. Mathematically, we can represent this as:

$$x - \frac{4}{3} = \frac{11}{3}$$

Q: How do I solve the equation? A: To find the value of $x$, we need to isolate it on one side of the equation. We can do this by adding $\frac{4}{3}$ to both sides of the equation. This will cancel out the $\frac{4}{3}$ on the left-hand side, leaving us with the value of $x$.

Q: What is the value of $x$? A: After simplifying the equation, we find that:

$$x = \frac{15}{3}$$

$$x = \frac{5}{1}$$

$$x = 5$$

Q: What are some real-world applications of this problem? A: While this problem may seem trivial, it has real-world applications in various fields such as finance, engineering, and science. For instance, in finance, understanding the difference between two values can help investors make informed decisions about their investments. In engineering, knowing the difference between two values can be crucial in designing and building complex systems.

Q: What are some common mistakes to avoid when solving equations? A: When solving equations, it's easy to make mistakes. Here are some common pitfalls to avoid:

• Forgetting to simplify fractions: Make sure to simplify fractions by dividing both the numerator and the denominator by their greatest common divisor.
• Not following the order of operations: Always follow the order of operations (PEMDAS) to ensure that you're solving equations correctly.
• Not checking your work: Double-check your work to ensure that you've solved the equation correctly.

Q: How can I practice solving equations? A: There are many resources available to help you practice solving equations. Here are a few suggestions:

• Math textbooks: Use math textbooks to practice solving equations.
• Online resources: Websites such as Khan Academy, Mathway, and Wolfram Alpha offer interactive math lessons and exercises to help you practice solving equations.
• Practice problems: Try solving practice problems from various sources to improve your skills.

Q: What are some tips for solving equations? A: Here are some tips to help you solve equations:

• Read the problem carefully: Make sure you understand what the problem is asking.
• Write an equation: Write an equation that describes the situation.
• Simplify the equation: Simplify the equation by combining like terms and canceling out any common factors.
• Check your work: Double-check your work to ensure that you've solved the equation correctly.

Conclusion

In this article, we have unraveled the mystery of the unknown number. By writing an equation that describes the situation, we were able to isolate the value of $x$ and find that it equals 5. This demonstrates the power of algebra in solving mathematical puzzles and equations. We hope that this article has been helpful in answering your questions and providing you with a better understanding of how to solve equations.