Solve: $\frac{1}{6} = -\frac{8}{3}r$

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Introduction

When solving equations involving fractions, it's essential to isolate the variable by getting rid of the fractions. In this case, we have an equation with a fraction on the left-hand side and a variable multiplied by a fraction on the right-hand side. Our goal is to solve for the variable $r$.

Understanding the Equation

The given equation is $\frac{1}{6} = -\frac{8}{3}r$. To solve for $r$, we need to get rid of the fraction on the right-hand side. We can do this by multiplying both sides of the equation by the reciprocal of the fraction on the right-hand side.

Multiplying Both Sides by the Reciprocal

The reciprocal of $-\frac{8}{3}$ is $-\frac{3}{8}$. To get rid of the fraction on the right-hand side, we multiply both sides of the equation by $-\frac{3}{8}$.

$\frac{1}{6} = -\frac{8}{3}r$

Multiplying both sides by $-\frac{3}{8}$:

$\frac{1}{6} \cdot -\frac{3}{8} = -\frac{8}{3}r \cdot -\frac{3}{8}$

Simplifying the left-hand side:

$-\frac{1}{16} = r$

Solving for $r$

Now that we have isolated the variable $r$, we can see that $r = -\frac{1}{16}$.

Conclusion

In this article, we solved the equation $\frac{1}{6} = -\frac{8}{3}r$ by getting rid of the fraction on the right-hand side. We multiplied both sides of the equation by the reciprocal of the fraction on the right-hand side and simplified the left-hand side to find the value of $r$. The final answer is $r = -\frac{1}{16}$.

Step-by-Step Solution

Here's a step-by-step solution to the equation:

1. Multiply both sides of the equation by the reciprocal of the fraction on the right-hand side:

$\frac{1}{6} = -\frac{8}{3}r$

Multiplying both sides by $-\frac{3}{8}$:

$\frac{1}{6} \cdot -\frac{3}{8} = -\frac{8}{3}r \cdot -\frac{3}{8}$

2. Simplify the left-hand side:

$-\frac{1}{16} = r$

Frequently Asked Questions

• Q: What is the value of $r$ in the equation $\frac{1}{6} = -\frac{8}{3}r$? A: The value of $r$ is $-\frac{1}{16}$.
• Q: How do I solve an equation with a fraction on the right-hand side? A: To solve an equation with a fraction on the right-hand side, multiply both sides of the equation by the reciprocal of the fraction on the right-hand side.

Related Topics

• Solving equations with fractions
• Multiplying fractions
• Reciprocals

Final Answer

The final answer is $r = -\frac{1}{16}$.

Introduction

Solving equations with fractions can be a challenging task, but with the right techniques and strategies, it can be made easier. In this article, we will answer some of the most frequently asked questions about solving equations with fractions.

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

A: The first step in solving an equation with a fraction is to get rid of the fraction on the right-hand side. This can be done by multiplying both sides of the equation by the reciprocal of the fraction on the right-hand side.

Q: How do I find the reciprocal of a fraction?

A: To find the reciprocal of a fraction, you need to flip the numerator and the denominator. For example, the reciprocal of $\frac{1}{2}$ is $\frac{2}{1}$, and the reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$.

Q: What is the difference between a reciprocal and a multiplicative inverse?

A: A reciprocal and a multiplicative inverse are the same thing. They are used interchangeably to refer to the number that, when multiplied by a given number, results in 1.

Q: Can I simplify an equation with a fraction before solving it?

A: Yes, you can simplify an equation with a fraction before solving it. Simplifying the equation can make it easier to solve and can also help you avoid making mistakes.

Q: How do I know if an equation with a fraction is linear or non-linear?

A: An equation with a fraction is linear if the variable is raised to the power of 1, and it is non-linear if the variable is raised to a power other than 1.

Q: Can I use the distributive property to solve an equation with a fraction?

A: Yes, you can use the distributive property to solve an equation with a fraction. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac.

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, and a quadratic equation is an equation in which the highest power of the variable is 2.

Q: Can I use algebraic manipulations to solve an equation with a fraction?

A: Yes, you can use algebraic manipulations to solve an equation with a fraction. Algebraic manipulations include adding, subtracting, multiplying, and dividing both sides of the equation by the same value.

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

A: To check your solution to an equation with a fraction, plug the solution back into the original equation and make sure it is true.

Q: Can I use a calculator to solve an equation with a fraction?

A: Yes, you can use a calculator to solve an equation with a fraction. However, make sure to check your solution to ensure it is correct.

Q: What are some common mistakes to avoid when solving equations with fractions?

A: Some common mistakes to avoid when solving equations with fractions include:

• Not getting rid of the fraction on the right-hand side
• Not simplifying the equation before solving it
• Not checking the solution to the equation
• Not using the correct algebraic manipulations to solve the equation

Conclusion

Solving equations with fractions can be a challenging task, but with the right techniques and strategies, it can be made easier. By following the steps outlined in this article and avoiding common mistakes, you can become proficient in solving equations with fractions.

Step-by-Step Solution

Here's a step-by-step solution to the equation:

1. Get rid of the fraction on the right-hand side by multiplying both sides of the equation by the reciprocal of the fraction on the right-hand side.
2. Simplify the equation before solving it.
3. Use algebraic manipulations to solve the equation.
4. Check the solution to the equation to ensure it is correct.

Frequently Asked Questions

• Q: What is the first step in solving an equation with a fraction? A: The first step in solving an equation with a fraction is to get rid of the fraction on the right-hand side.
• Q: How do I find the reciprocal of a fraction? A: To find the reciprocal of a fraction, you need to flip the numerator and the denominator.
• Q: What is the difference between a reciprocal and a multiplicative inverse? A: A reciprocal and a multiplicative inverse are the same thing.

Related Topics

• Solving equations with fractions
• Multiplying fractions
• Reciprocals
• Algebraic manipulations

Final Answer

The final answer is that solving equations with fractions requires getting rid of the fraction on the right-hand side, simplifying the equation, and using algebraic manipulations to solve the equation.