Solve For \[$ T \$\].$\[ T - \frac{2}{3} = \frac{5}{6} \\]

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Introduction

In mathematics, solving for a variable is a crucial skill that helps us understand and manipulate equations. One of the most common variables we encounter is time, denoted by the letter t. In this article, we will focus on solving for t in the equation t - 2/3 = 5/6. We will break down the solution into manageable steps, making it easy to follow and understand.

Understanding the Equation

The given equation is t - 2/3 = 5/6. To solve for t, we need to isolate the variable t on one side of the equation. The equation involves fractions, which can be challenging to work with. However, with the right approach, we can simplify the equation and find the value of t.

Step 1: Add 2/3 to Both Sides of the Equation

To isolate t, we need to get rid of the -2/3 on the left side of the equation. We can do this by adding 2/3 to both sides of the equation. This will keep the equation balanced and ensure that we are not changing the value of t.

t - 2/3 + 2/3 = 5/6 + 2/3

Step 2: Simplify the Right Side of the Equation

Now that we have added 2/3 to both sides of the equation, we can simplify the right side. To add fractions, we need to have the same denominator. In this case, the denominators are 6 and 3. We can convert 2/3 to have a denominator of 6 by multiplying both the numerator and denominator by 2.

2/3 = 4/6

Now we can add 5/6 and 4/6.

5/6 + 4/6 = 9/6

Step 3: Simplify the Right Side of the Equation (Continued)

The right side of the equation is now 9/6. However, we can simplify this fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 3.

9/6 = 3/2

Step 4: Write the Final Equation

Now that we have simplified the right side of the equation, we can write the final equation.

t = 3/2

Conclusion

Solving for t in the equation t - 2/3 = 5/6 requires careful manipulation of fractions. By adding 2/3 to both sides of the equation and simplifying the right side, we can isolate t and find its value. In this case, the value of t is 3/2.

Tips and Tricks

  • When working with fractions, it's essential to have the same denominator to add or subtract them.
  • To simplify a fraction, divide both the numerator and denominator by their greatest common divisor.
  • When solving for a variable, make sure to isolate it on one side of the equation.

Real-World Applications

Solving for time is a crucial skill in various real-world applications, such as:

  • Physics: When calculating the time it takes for an object to travel a certain distance.
  • Engineering: When designing systems that involve time-dependent variables.
  • Economics: When analyzing the impact of time on economic models.

Final Thoughts

Solving for t in the equation t - 2/3 = 5/6 may seem challenging at first, but with the right approach, it's achievable. By breaking down the solution into manageable steps and simplifying fractions, we can isolate t and find its value. This skill is essential in various real-world applications, and with practice, you can become proficient in solving for time.

Introduction

In our previous article, we explored the step-by-step process of solving for t in the equation t - 2/3 = 5/6. However, we understand that sometimes, a more interactive approach can be helpful. That's why we've created this Q&A guide to address common questions and concerns about solving for time.

Q: What is the first step in solving for t in the equation t - 2/3 = 5/6?

A: The first step is to add 2/3 to both sides of the equation. This will help us isolate t and get rid of the -2/3 on the left side of the equation.

Q: Why do we need to have the same denominator when adding fractions?

A: When adding fractions, we need to have the same denominator to ensure that we are adding the same quantities. In this case, we can convert 2/3 to have a denominator of 6 by multiplying both the numerator and denominator by 2.

Q: How do we simplify the right side of the equation?

A: To simplify the right side of the equation, we can divide both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of 9 and 6 is 3, so we can simplify the fraction 9/6 to 3/2.

Q: What is the final value of t in the equation t - 2/3 = 5/6?

A: The final value of t is 3/2.

Q: Can we use this method to solve for t in other equations?

A: Yes, this method can be applied to solve for t in other equations that involve fractions. However, the specific steps may vary depending on the equation.

Q: What are some real-world applications of solving for time?

A: Solving for time is a crucial skill in various real-world applications, such as physics, engineering, and economics. It can be used to calculate the time it takes for an object to travel a certain distance, design systems that involve time-dependent variables, and analyze the impact of time on economic models.

Q: How can I practice solving for time?

A: You can practice solving for time by working on sample problems and exercises. Start with simple equations and gradually move on to more complex ones. You can also use online resources and practice tests to help you improve your skills.

Q: What are some common mistakes to avoid when solving for time?

A: Some common mistakes to avoid when solving for time include:

  • Not having the same denominator when adding fractions
  • Not simplifying fractions correctly
  • Not isolating the variable t on one side of the equation
  • Not checking the final answer for accuracy

Conclusion

Solving for time is a crucial skill that can be applied to various real-world applications. By following the steps outlined in this Q&A guide, you can improve your skills and become proficient in solving for time. Remember to practice regularly and avoid common mistakes to ensure accuracy and success.

Additional Resources

  • Online practice tests and exercises
  • Sample problems and solutions
  • Online resources and tutorials
  • Math textbooks and workbooks

Final Thoughts

Solving for time is a challenging but rewarding skill that can be applied to various real-world applications. By practicing regularly and avoiding common mistakes, you can become proficient in solving for time and achieve success in your math and science studies.