Solve For $h$.$2 \frac{1}{8} = H + \frac{5}{8}$$ H = H = H = [/tex]
Introduction
In mathematics, solving for a 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 h in the equation 2 1/8 = h + 5/8. This equation involves fractions and mixed numbers, and we will use algebraic techniques to isolate the variable h.
Understanding the Equation
The given equation is 2 1/8 = h + 5/8. To start solving for h, we need to understand the equation and identify the variable. In this equation, h is the variable that we need to solve for. The other terms in the equation are constants, and we will use algebraic techniques to isolate the variable h.
Converting Mixed Numbers to Improper Fractions
To solve for h, we need to convert the mixed number 2 1/8 to an improper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we multiply the whole number part by the denominator and add the numerator. In this case, we have 2 1/8, which can be converted to an improper fraction as follows:
2 1/8 = (2 × 8) + 1/8 = 16 + 1/8 = 17/8
Substituting the Improper Fraction into the Equation
Now that we have converted the mixed number 2 1/8 to an improper fraction, we can substitute it into the equation:
17/8 = h + 5/8
Subtracting 5/8 from Both Sides
To isolate the variable h, we need to subtract 5/8 from both sides of the equation. This will allow us to get rid of the constant term on the right-hand side of the equation. To subtract 5/8 from 17/8, we need to find a common denominator, which is 8. Since both fractions already have a denominator of 8, we can subtract them directly:
17/8 - 5/8 = (17 - 5)/8 = 12/8
Simplifying the Fraction
The fraction 12/8 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4. This will give us:
12/8 = 3/2
Conclusion
In this article, we solved for the variable h in the equation 2 1/8 = h + 5/8. We started by converting the mixed number 2 1/8 to an improper fraction, which is 17/8. We then substituted this improper fraction into the equation and subtracted 5/8 from both sides to isolate the variable h. Finally, we simplified the fraction 12/8 to get the final answer, which is 3/2.
Final Answer
The final answer to the equation 2 1/8 = h + 5/8 is:
h = 3/2
Real-World Applications
Solving for a variable is a fundamental concept in mathematics that has many real-world applications. In science, technology, engineering, and mathematics (STEM) fields, solving for a variable is used to model real-world problems and make predictions. For example, in physics, solving for a variable can help us understand the motion of objects and make predictions about their behavior. In economics, solving for a variable can help us understand the behavior of markets and make predictions about future trends.
Tips and Tricks
Here are some tips and tricks for solving for a variable:
- Always start by identifying the variable and the constants in the equation.
- Use algebraic techniques such as addition, subtraction, multiplication, and division to isolate the variable.
- Be careful when working with fractions and mixed numbers, as they can be tricky to work with.
- Use a calculator or a computer program to check your answers and make sure that you have solved for the variable correctly.
Common Mistakes
Here are some common mistakes to avoid when solving for a variable:
- Not identifying the variable and the constants in the equation.
- Not using algebraic techniques to isolate the variable.
- Not being careful when working with fractions and mixed numbers.
- Not checking your answers to make sure that you have solved for the variable correctly.
Conclusion
Solving for a variable is a fundamental concept in mathematics that has many real-world applications. In this article, we solved for the variable h in the equation 2 1/8 = h + 5/8. We started by converting the mixed number 2 1/8 to an improper fraction, which is 17/8. We then substituted this improper fraction into the equation and subtracted 5/8 from both sides to isolate the variable h. Finally, we simplified the fraction 12/8 to get the final answer, which is 3/2.
Introduction
In our previous article, we solved for the variable h in the equation 2 1/8 = h + 5/8. In this article, we will answer some frequently asked questions about solving for a variable and provide additional tips and tricks for solving equations.
Q: What is the first step in solving for a variable?
A: The first step in solving for a variable is to identify the variable and the constants in the equation. In the equation 2 1/8 = h + 5/8, the variable is h and the constants are 2 1/8 and 5/8.
Q: How do I convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, you multiply the whole number part by the denominator and add the numerator. For example, to convert 2 1/8 to an improper fraction, you would multiply 2 by 8 and add 1, which gives you 17/8.
Q: What is the difference between a fraction and a mixed number?
A: A fraction is a number that represents a part of a whole, and it is written in the form a/b, where a is the numerator and b is the denominator. A mixed number is a combination of a whole number and a fraction, and it is written in the form a b/c, where a is the whole number part and b/c is the fraction part.
Q: How do I subtract fractions with different denominators?
A: To subtract fractions with different denominators, you need to find a common denominator. The common denominator is the smallest number that both denominators can divide into evenly. For example, to subtract 1/2 and 1/4, you would find the common denominator, which is 4. Then, you would rewrite the fractions with the common denominator: 2/4 - 1/4 = 1/4.
Q: What is the final answer to the equation 2 1/8 = h + 5/8?
A: The final answer to the equation 2 1/8 = h + 5/8 is h = 3/2.
Q: How do I check my answer to make sure that I have solved for the variable correctly?
A: To check your answer, you can plug the value of the variable back into the original equation and see if it is true. For example, if you think that h = 3/2 is the solution to the equation 2 1/8 = h + 5/8, you can plug 3/2 back into the equation and see if it is true.
Q: What are some common mistakes to avoid when solving for a variable?
A: Some common mistakes to avoid when solving for a variable include not identifying the variable and the constants in the equation, not using algebraic techniques to isolate the variable, and not being careful when working with fractions and mixed numbers.
Q: How do I use algebraic techniques to isolate the variable?
A: Algebraic techniques include addition, subtraction, multiplication, and division. To isolate the variable, you need to use these techniques to get the variable by itself on one side of the equation. For example, in the equation 2 1/8 = h + 5/8, you can subtract 5/8 from both sides to isolate the variable h.
Q: What are some real-world applications of solving for a variable?
A: Solving for a variable has many real-world applications, including science, technology, engineering, and mathematics (STEM) fields. For example, in physics, solving for a variable can help us understand the motion of objects and make predictions about their behavior. In economics, solving for a variable can help us understand the behavior of markets and make predictions about future trends.
Q: How do I use a calculator or computer program to check my answer?
A: To use a calculator or computer program to check your answer, you can plug the value of the variable back into the original equation and see if it is true. For example, if you think that h = 3/2 is the solution to the equation 2 1/8 = h + 5/8, you can plug 3/2 back into the equation and see if it is true.
Conclusion
Solving for a variable is a fundamental concept in mathematics that has many real-world applications. In this article, we answered some frequently asked questions about solving for a variable and provided additional tips and tricks for solving equations. We also discussed some common mistakes to avoid when solving for a variable and how to use algebraic techniques to isolate the variable.