Solve For \[$ U \$\]:$\[ 5 \frac{1}{2} - U = \frac{9}{4} \\]

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Solving for the Unknown Variable: A Step-by-Step Guide to Isolate u

In mathematics, solving for an unknown variable is a fundamental concept that involves isolating the variable on one side of the equation. In this article, we will focus on solving for the variable u in the given equation: 512−u=945 \frac{1}{2} - u = \frac{9}{4}. We will break down the solution into manageable steps, making it easy to understand and follow along.

Understanding the Equation

The given equation is 512−u=945 \frac{1}{2} - u = \frac{9}{4}. To start solving for u, we need to understand the equation and identify the variable we want to isolate. In this case, the variable is u.

Converting Mixed Numbers to Improper Fractions

The first step in solving the equation is to convert the mixed number 5125 \frac{1}{2} to an improper fraction. To do this, we multiply the whole number part (5) by the denominator (2) and then add the numerator (1). This gives us:

512=(5×2)+12=1125 \frac{1}{2} = \frac{(5 \times 2) + 1}{2} = \frac{11}{2}

Now that we have converted the mixed number to an improper fraction, we can rewrite the equation as:

112−u=94\frac{11}{2} - u = \frac{9}{4}

Finding a Common Denominator

To simplify the equation and make it easier to solve, we need to find a common denominator for the fractions. The least common multiple (LCM) of 2 and 4 is 4. Therefore, we can rewrite the fractions with a common denominator of 4:

112=11×22×2=224\frac{11}{2} = \frac{11 \times 2}{2 \times 2} = \frac{22}{4}

Now that we have a common denominator, we can rewrite the equation as:

224−u=94\frac{22}{4} - u = \frac{9}{4}

Isolating the Variable u

To isolate the variable u, we need to get rid of the fraction on the left side of the equation. We can do this by subtracting 224\frac{22}{4} from both sides of the equation:

−u=94−224-u = \frac{9}{4} - \frac{22}{4}

Simplifying the right side of the equation, we get:

−u=−134-u = -\frac{13}{4}

Solving for u

To solve for u, we need to get rid of the negative sign in front of the variable. We can do this by multiplying both sides of the equation by -1:

u=134u = \frac{13}{4}

Conclusion

In this article, we solved for the variable u in the given equation 512−u=945 \frac{1}{2} - u = \frac{9}{4}. We broke down the solution into manageable steps, making it easy to understand and follow along. We converted the mixed number to an improper fraction, found a common denominator, isolated the variable u, and finally solved for u. The final solution is u=134u = \frac{13}{4}.

Frequently Asked Questions

  • What is the value of u in the given equation? The value of u in the given equation is 134\frac{13}{4}.
  • How do I convert a mixed number to an improper fraction? To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and then add the numerator.
  • How do I find a common denominator for fractions? To find a common denominator for fractions, find the least common multiple (LCM) of the denominators.

Additional Resources

  • Mathematics Formulas and Equations: A comprehensive guide to mathematics formulas and equations.
  • Solving Linear Equations: A step-by-step guide to solving linear equations.
  • Mathematics Tutorials: A collection of mathematics tutorials and resources.
    Solving for the Unknown Variable: A Q&A Guide

In our previous article, we solved for the variable u in the given equation 512−u=945 \frac{1}{2} - u = \frac{9}{4}. We broke down the solution into manageable steps, making it easy to understand and follow along. In this article, we will provide a Q&A guide to help you better understand the concept of solving for an unknown variable.

Q&A Guide

Q: What is the first step in solving for an unknown variable? A: The first step in solving for an unknown variable is to understand the equation and identify the variable we want to isolate.

Q: How do I convert a mixed number to an improper fraction? A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and then add the numerator.

Q: What is the least common multiple (LCM) and how do I find it? A: The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. To find the LCM, list the multiples of each number and find the smallest number that appears in both lists.

Q: How do I find a common denominator for fractions? A: To find a common denominator for fractions, find the least common multiple (LCM) of the denominators.

Q: What is the difference between a linear equation and a quadratic equation? A: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I solve a linear equation? A: To solve a linear equation, follow these steps:

  1. Simplify the equation by combining like terms.
  2. Isolate the variable by adding or subtracting the same value to both sides of the equation.
  3. Multiply or divide both sides of the equation by the same value to eliminate the coefficient of the variable.

Q: What is the order of operations in mathematics? A: The order of operations in mathematics is:

  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.

Real-World Applications

Solving for an unknown variable is a fundamental concept in mathematics that has many real-world applications. Here are a few examples:

  • Physics: In physics, solving for an unknown variable is used to calculate the position, velocity, and acceleration of objects.
  • Engineering: In engineering, solving for an unknown variable is used to design and optimize systems, such as bridges, buildings, and electronic circuits.
  • Economics: In economics, solving for an unknown variable is used to model and analyze economic systems, such as supply and demand curves.

Conclusion

In this article, we provided a Q&A guide to help you better understand the concept of solving for an unknown variable. We covered topics such as converting mixed numbers to improper fractions, finding a common denominator, and solving linear equations. We also discussed the order of operations in mathematics and provided real-world applications of solving for an unknown variable.

Frequently Asked Questions

  • What is the value of u in the given equation? The value of u in the given equation is 134\frac{13}{4}.
  • How do I convert a mixed number to an improper fraction? To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and then add the numerator.
  • How do I find a common denominator for fractions? To find a common denominator for fractions, find the least common multiple (LCM) of the denominators.

Additional Resources

  • Mathematics Formulas and Equations: A comprehensive guide to mathematics formulas and equations.
  • Solving Linear Equations: A step-by-step guide to solving linear equations.
  • Mathematics Tutorials: A collection of mathematics tutorials and resources.