Solve M 4 + 6 = 14 \frac{m}{4} + 6 = 14 4 M ​ + 6 = 14

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Introduction

Mathematics is a fundamental subject that plays a crucial role in our daily lives. It is a subject that deals with numbers, quantities, and shapes. In mathematics, we often come across equations that need to be solved to find the value of a variable. In this article, we will focus on solving a simple equation involving fractions.

Understanding the Equation

The given equation is $\frac{m}{4} + 6 = 14$. This equation involves a fraction and a constant term. To solve for the variable $m$, we need to isolate it on one side of the equation.

Isolating the Fraction

To isolate the fraction, we need to get rid of the constant term on the same side as the fraction. We can do this by subtracting 6 from both sides of the equation.

$\frac{m}{4} + 6 - 6 = 14 - 6$

This simplifies to:

$\frac{m}{4} = 8$

Eliminating the Fraction

To eliminate the fraction, we need to multiply both sides of the equation by the denominator, which is 4.

$\frac{m}{4} \times 4 = 8 \times 4$

This simplifies to:

$m = 32$

Conclusion

In this article, we solved the equation $\frac{m}{4} + 6 = 14$ to find the value of the variable $m$. We started by isolating the fraction and then eliminated it by multiplying both sides of the equation by the denominator. The final answer is $m = 32$.

Tips and Tricks

• When solving equations involving fractions, it is essential to isolate the fraction first.
• To eliminate the fraction, multiply both sides of the equation by the denominator.
• Always check your work by plugging the solution back into the original equation.

Real-World Applications

Solving equations involving fractions has numerous real-world applications. For example, in finance, we often come across equations that involve fractions, such as calculating interest rates or investment returns. In science, we use equations involving fractions to model real-world phenomena, such as the motion of objects or the behavior of chemical reactions.

Common Mistakes

• Failing to isolate the fraction before eliminating it.
• Multiplying both sides of the equation by the wrong denominator.
• Not checking the solution by plugging it back into the original equation.

Final Thoughts

Solving equations involving fractions is a fundamental skill that is essential in mathematics and real-world applications. By following the steps outlined in this article, you can confidently solve equations involving fractions and apply them to real-world problems.

Additional Resources

• Khan Academy: Solving Equations with Fractions
• Mathway: Solving Equations with Fractions
• Wolfram Alpha: Solving Equations with Fractions

Frequently Asked Questions

• Q: What is the first step in solving an equation involving a fraction? A: The first step is to isolate the fraction.
• Q: How do I eliminate a fraction in an equation? A: Multiply both sides of the equation by the denominator.
• Q: Why is it essential to check the solution by plugging it back into the original equation? A: To ensure that the solution is correct and accurate.

Conclusion

Solving equations involving fractions is a fundamental skill that is essential in mathematics and real-world applications. By following the steps outlined in this article, you can confidently solve equations involving fractions and apply them to real-world problems. Remember to isolate the fraction first, eliminate it by multiplying both sides of the equation by the denominator, and check the solution by plugging it back into the original equation.

Introduction

Solving equations involving fractions can be a challenging task, but with the right guidance, it can be made easier. In this article, we will address some of the most frequently asked questions related to solving equations involving fractions.

Q&A

Q: What is the first step in solving an equation involving a fraction?

A: The first step is to isolate the fraction. This means getting the fraction by itself on one side of the equation, away from any other terms.

Q: How do I isolate the fraction in an equation?

A: To isolate the fraction, you need to get rid of any terms that are not part of the fraction. This can be done by adding or subtracting the same value to both sides of the equation.

Q: What is the next step after isolating the fraction?

A: After isolating the fraction, the next step is to eliminate the fraction. This can be done by multiplying both sides of the equation by the denominator.

Q: How do I eliminate the fraction in an equation?

A: To eliminate the fraction, multiply both sides of the equation by the denominator. This will get rid of the fraction and leave you with a whole number equation.

Q: What is the most common mistake people make when solving equations involving fractions?

A: The most common mistake people make is failing to isolate the fraction before eliminating it. This can lead to incorrect solutions and a lot of frustration.

Q: How do I check my solution to an equation involving a fraction?

A: To check your solution, plug it back into the original equation and see if it is true. If it is true, then your solution is correct. If it is not true, then you need to go back and rework the equation.

Q: What are some real-world applications of solving equations involving fractions?

A: Solving equations involving fractions has numerous real-world applications. For example, in finance, we often come across equations that involve fractions, such as calculating interest rates or investment returns. In science, we use equations involving fractions to model real-world phenomena, such as the motion of objects or the behavior of chemical reactions.

Q: Can you provide some examples of equations involving fractions that I can practice solving?

A: Here are a few examples of equations involving fractions that you can practice solving:

• $\frac{x}{2} + 3 = 7$
• $\frac{y}{4} - 2 = 5$
• $\frac{z}{6} + 1 = 9$

Q: What are some tips for solving equations involving fractions?

A: Here are a few tips for solving equations involving fractions:

• Always isolate the fraction first.
• Multiply both sides of the equation by the denominator to eliminate the fraction.
• Check your solution by plugging it back into the original equation.
• Practice, practice, practice!

Conclusion

Solving equations involving fractions can be a challenging task, but with the right guidance, it can be made easier. By following the steps outlined in this article and practicing with examples, you can become proficient in solving equations involving fractions. Remember to isolate the fraction first, eliminate it by multiplying both sides of the equation by the denominator, and check the solution by plugging it back into the original equation.

Additional Resources

• Khan Academy: Solving Equations with Fractions
• Mathway: Solving Equations with Fractions
• Wolfram Alpha: Solving Equations with Fractions

Frequently Asked Questions (FAQs)

• Q: What is the difference between a fraction and a decimal? A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a decimal is a way of expressing a number as a sum of powers of 10.
• Q: How do I convert a fraction to a decimal? A: To convert a fraction to a decimal, divide the numerator by the denominator.
• 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.

Conclusion

Solving equations involving fractions is a fundamental skill that is essential in mathematics and real-world applications. By following the steps outlined in this article and practicing with examples, you can become proficient in solving equations involving fractions. Remember to isolate the fraction first, eliminate it by multiplying both sides of the equation by the denominator, and check the solution by plugging it back into the original equation.