Solve For M M M In The Equation 3 2 = 1 3 M \frac{3}{2}=\frac{1}{3} M 2 3 ​ = 3 1 ​ M .A. − 1 3 -\frac{1}{3} − 3 1 ​ B. 7 6 \frac{7}{6} 6 7 ​ C. 1 2 \frac{1}{2} 2 1 ​ D. 9 2 \frac{9}{2} 2 9 ​

Solving for $m$ in the Equation $\frac{3}{2}=\frac{1}{3} m$

Understanding the Problem

The given equation is $\frac{3}{2}=\frac{1}{3} m$. To solve for $m$, we need to isolate the variable $m$ on one side of the equation. This involves performing algebraic operations to simplify the equation and find the value of $m$.

Step 1: Multiply Both Sides by 3

To eliminate the fraction on the right-hand side, we can multiply both sides of the equation by 3. This will give us:

$$\frac{3}{2} \cdot 3 = \frac{1}{3} m \cdot 3$$

Simplifying the left-hand side, we get:

$$\frac{9}{2} = m$$

However, this is not the correct solution. We need to revisit the steps and ensure that we are performing the correct operations.

Step 2: Multiply Both Sides by 3

Let's revisit the first step and multiply both sides of the equation by 3:

$$\frac{3}{2} \cdot 3 = \frac{1}{3} m \cdot 3$$

This gives us:

$$\frac{9}{2} = m$$

But we are not done yet. We need to check if this solution is correct.

Step 3: Check the Solution

To check the solution, we can substitute the value of $m$ back into the original equation:

$$\frac{3}{2} = \frac{1}{3} \left(\frac{9}{2}\right)$$

Simplifying the right-hand side, we get:

$$\frac{3}{2} = \frac{3}{2}$$

This shows that the solution is correct.

Conclusion

The correct solution to the equation $\frac{3}{2}=\frac{1}{3} m$ is $\frac{9}{2}$. This can be verified by substituting the value of $m$ back into the original equation.

Answer

The correct answer is:

• D. $\frac{9}{2}$

Explanation

To solve for $m$, we need to isolate the variable $m$ on one side of the equation. This involves performing algebraic operations to simplify the equation and find the value of $m$. In this case, we multiplied both sides of the equation by 3 to eliminate the fraction on the right-hand side. This gave us the solution $\frac{9}{2}$, which can be verified by substituting the value of $m$ back into the original equation.

Tips and Tricks

• When solving equations, it's essential to check the solution by substituting the value of the variable back into the original equation.
• Make sure to perform the correct algebraic operations to simplify the equation and find the value of the variable.
• Use multiplication and division to eliminate fractions and simplify the equation.

Common Mistakes

• Failing to check the solution by substituting the value of the variable back into the original equation.
• Performing incorrect algebraic operations to simplify the equation and find the value of the variable.
• Not using multiplication and division to eliminate fractions and simplify the equation.

Real-World Applications

• Solving equations is a fundamental concept in mathematics and has numerous real-world applications, such as:

• Calculating the area and perimeter of shapes
• Determining the cost and profit of a business
• Solving problems in physics and engineering

Conclusion

Solving for $m$ in the equation $\frac{3}{2}=\frac{1}{3} m$ requires careful algebraic operations and attention to detail. By following the steps outlined in this article, you can find the correct solution and verify it by substituting the value of $m$ back into the original equation.
Solving for $m$ in the Equation $\frac{3}{2}=\frac{1}{3} m$: Q&A

Q: What is the first step in solving the equation $\frac{3}{2}=\frac{1}{3} m$?

A: The first step in solving the equation is to multiply both sides of the equation by 3 to eliminate the fraction on the right-hand side.

Q: Why do we multiply both sides of the equation by 3?

A: We multiply both sides of the equation by 3 to eliminate the fraction on the right-hand side. This is because multiplying both sides of the equation by the same value will not change the equation, but it will allow us to simplify the equation and find the value of $m$.

Q: What is the next step in solving the equation?

A: After multiplying both sides of the equation by 3, we need to simplify the equation and find the value of $m$. This involves performing algebraic operations to isolate the variable $m$ on one side of the equation.

Q: How do we simplify the equation and find the value of $m$?

A: To simplify the equation and find the value of $m$, we need to perform algebraic operations such as multiplication and division. We can multiply both sides of the equation by the reciprocal of the coefficient of $m$ to isolate the variable $m$ on one side of the equation.

Q: What is the final step in solving the equation?

A: The final step in solving the equation is to check the solution by substituting the value of $m$ back into the original equation. This ensures that the solution is correct and that we have not made any errors in our calculations.

Q: Why is it essential to check the solution?

A: It is essential to check the solution because it ensures that the solution is correct and that we have not made any errors in our calculations. If we do not check the solution, we may end up with an incorrect answer, which can have serious consequences in real-world applications.

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

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

• Failing to check the solution by substituting the value of the variable back into the original equation.
• Performing incorrect algebraic operations to simplify the equation and find the value of the variable.
• Not using multiplication and division to eliminate fractions and simplify the equation.

Q: How can we apply the concept of solving equations to real-world problems?

A: The concept of solving equations can be applied to real-world problems in a variety of ways, such as:

• Calculating the area and perimeter of shapes
• Determining the cost and profit of a business
• Solving problems in physics and engineering

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

A: Some tips and tricks for solving equations include:

• Using multiplication and division to eliminate fractions and simplify the equation.
• Checking the solution by substituting the value of the variable back into the original equation.
• Being careful when performing algebraic operations to avoid errors.

Q: How can we use technology to help us solve equations?

A: Technology can be used to help us solve equations in a variety of ways, such as:

• Using calculators to perform calculations and simplify the equation.
• Using computer software to solve equations and check the solution.
• Using online resources and tutorials to learn how to solve equations.

Conclusion

Solving for $m$ in the equation $\frac{3}{2}=\frac{1}{3} m$ requires careful algebraic operations and attention to detail. By following the steps outlined in this article and avoiding common mistakes, you can find the correct solution and apply the concept of solving equations to real-world problems.