Solve For \[$ A \$\] In The Equation:$\[ \frac{7}{10} - A = \frac{1}{2} \\]

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Introduction

In mathematics, solving equations is a fundamental concept that involves isolating the variable of interest. In this article, we will focus on solving for a in the equation $\frac{7}{10} - a = \frac{1}{2}$. This equation involves fractions, and we will use algebraic techniques to isolate the variable a.

Understanding the Equation

The given equation is $\frac{7}{10} - a = \frac{1}{2}$. To solve for a, we need to isolate the variable a on one side of the equation. The equation involves fractions, and we will use the properties of fractions to simplify the equation.

Simplifying the Equation

To simplify the equation, we can start by getting rid of the fraction on the left-hand side. We can do this by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is 10.

$\frac{7}{10} - a = \frac{1}{2}$

Multiplying both sides by 10:

$7 - 10a = 5$

Isolating the Variable a

Now that we have simplified the equation, we can isolate the variable a. We can do this by subtracting 7 from both sides of the equation and then dividing both sides by -10.

$7 - 10a = 5$

Subtracting 7 from both sides:

$-10a = -2$

Dividing both sides by -10:

$a = \frac{2}{10}$

Simplifying the Fraction

The fraction $\frac{2}{10}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2.

$a = \frac{2}{10}$

Dividing both the numerator and the denominator by 2:

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

Conclusion

In this article, we solved for a in the equation $\frac{7}{10} - a = \frac{1}{2}$. We started by simplifying the equation by getting rid of the fraction on the left-hand side. Then, we isolated the variable a by subtracting 7 from both sides and dividing both sides by -10. Finally, we simplified the fraction $\frac{2}{10}$ by dividing both the numerator and the denominator by their greatest common divisor. The solution to the equation is $a = \frac{1}{5}$.

Frequently Asked Questions

• What is the value of a in the equation $\frac{7}{10} - a = \frac{1}{2}$?
• How do you solve for a in an equation involving fractions?
• What is the least common multiple (LCM) of the denominators in the equation $\frac{7}{10} - a = \frac{1}{2}$?
• How do you simplify a fraction by dividing both the numerator and the denominator by their greatest common divisor?

Step-by-Step Solution

1. Simplify the equation by getting rid of the fraction on the left-hand side.
2. Isolate the variable a by subtracting 7 from both sides and dividing both sides by -10.
3. Simplify the fraction $\frac{2}{10}$ by dividing both the numerator and the denominator by their greatest common divisor.

Real-World Applications

Solving equations involving fractions is an essential skill in mathematics and has numerous real-world applications. For example, in finance, solving equations involving fractions can help calculate interest rates and investment returns. In science, solving equations involving fractions can help model population growth and chemical reactions.

Tips and Tricks

• When solving equations involving fractions, it's essential to get rid of the fraction on the left-hand side by multiplying both sides by the least common multiple (LCM) of the denominators.
• When isolating the variable a, make sure to subtract the constant term from both sides and then divide both sides by the coefficient of the variable.
• When simplifying fractions, make sure to divide both the numerator and the denominator by their greatest common divisor.

Conclusion

Solving for a in the equation $\frac{7}{10} - a = \frac{1}{2}$ requires a step-by-step approach. We started by simplifying the equation by getting rid of the fraction on the left-hand side. Then, we isolated the variable a by subtracting 7 from both sides and dividing both sides by -10. Finally, we simplified the fraction $\frac{2}{10}$ by dividing both the numerator and the denominator by their greatest common divisor. The solution to the equation is $a = \frac{1}{5}$.

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Introduction

In our previous article, we solved for a in the equation $\frac{7}{10} - a = \frac{1}{2}$. We used algebraic techniques to isolate the variable a and found that the solution to the equation is $a = \frac{1}{5}$. In this article, we will answer some frequently asked questions related to solving equations involving fractions.

Q&A

Q: What is the value of a in the equation $\frac{7}{10} - a = \frac{1}{2}$?

A: The value of a in the equation $\frac{7}{10} - a = \frac{1}{2}$ is $a = \frac{1}{5}$.

Q: How do you solve for a in an equation involving fractions?

A: To solve for a in an equation involving fractions, you need to get rid of the fraction on the left-hand side by multiplying both sides by the least common multiple (LCM) of the denominators. Then, you can isolate the variable a by subtracting the constant term from both sides and dividing both sides by the coefficient of the variable.

Q: What is the least common multiple (LCM) of the denominators in the equation $\frac{7}{10} - a = \frac{1}{2}$?

A: The least common multiple (LCM) of the denominators in the equation $\frac{7}{10} - a = \frac{1}{2}$ is 10.

Q: How do you simplify a fraction by dividing both the numerator and the denominator by their greatest common divisor?

A: To simplify a fraction by dividing both the numerator and the denominator by their greatest common divisor, you need to find the greatest common divisor (GCD) of the numerator and the denominator. Then, you can divide both the numerator and the denominator by the GCD to simplify the fraction.

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, solving equations involving fractions can help calculate interest rates and investment returns. In science, solving equations involving fractions can help model population growth and chemical reactions.

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

A: Some tips and tricks for solving equations involving fractions include:

• Getting rid of the fraction on the left-hand side by multiplying both sides by the least common multiple (LCM) of the denominators.
• Isolating the variable a by subtracting the constant term from both sides and dividing both sides by the coefficient of the variable.
• Simplifying fractions by dividing both the numerator and the denominator by their greatest common divisor.

Conclusion

Solving for a in the equation $\frac{7}{10} - a = \frac{1}{2}$ requires a step-by-step approach. We used algebraic techniques to isolate the variable a and found that the solution to the equation is $a = \frac{1}{5}$. In this article, we answered some frequently asked questions related to solving equations involving fractions. We hope that this article has been helpful in understanding how to solve equations involving fractions.

Frequently Asked Questions

• What is the value of a in the equation $\frac{7}{10} - a = \frac{1}{2}$?
• How do you solve for a in an equation involving fractions?
• What is the least common multiple (LCM) of the denominators in the equation $\frac{7}{10} - a = \frac{1}{2}$?
• How do you simplify a fraction by dividing both the numerator and the denominator by their greatest common divisor?
• What are some real-world applications of solving equations involving fractions?
• What are some tips and tricks for solving equations involving fractions?

Step-by-Step Solution

1. Simplify the equation by getting rid of the fraction on the left-hand side.
2. Isolate the variable a by subtracting the constant term from both sides and dividing both sides by the coefficient of the variable.
3. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.

Real-World Applications

Solving equations involving fractions has numerous real-world applications. For example, in finance, solving equations involving fractions can help calculate interest rates and investment returns. In science, solving equations involving fractions can help model population growth and chemical reactions.

Tips and Tricks

• When solving equations involving fractions, it's essential to get rid of the fraction on the left-hand side by multiplying both sides by the least common multiple (LCM) of the denominators.
• When isolating the variable a, make sure to subtract the constant term from both sides and then divide both sides by the coefficient of the variable.
• When simplifying fractions, make sure to divide both the numerator and the denominator by their greatest common divisor.

Conclusion

Solving for a in the equation $\frac{7}{10} - a = \frac{1}{2}$ requires a step-by-step approach. We used algebraic techniques to isolate the variable a and found that the solution to the equation is $a = \frac{1}{5}$. In this article, we answered some frequently asked questions related to solving equations involving fractions. We hope that this article has been helpful in understanding how to solve equations involving fractions.