Solve For \[$ M \$\].$\[ 12 \cdot M = \frac{1}{2} (6, 10) \\]
Introduction to the Problem
When dealing with mathematical equations, it's essential to understand the problem and the variables involved. In this case, we're given an equation that involves a variable { m $}$, and we need to solve for its value. The equation is { 12 \cdot m = \frac{1}{2} (6, 10) }$. To solve for { m $}$, we need to isolate the variable and find its value.
Understanding the Equation
The given equation is { 12 \cdot m = \frac{1}{2} (6, 10) }$. This equation involves a multiplication operation on the left-hand side and a division operation on the right-hand side. The variable { m $}$ is multiplied by 12, and the result is equal to half of the sum of 6 and 10.
Breaking Down the Equation
To solve for { m $}$, we need to break down the equation and simplify it. The first step is to evaluate the expression on the right-hand side of the equation. The expression { \frac{1}{2} (6, 10) }$ represents half of the sum of 6 and 10.
Evaluating the Expression
To evaluate the expression { \frac{1}{2} (6, 10) }$, we need to follow the order of operations (PEMDAS). First, we need to add 6 and 10, and then divide the result by 2.
Calculating the Sum
The sum of 6 and 10 is { 6 + 10 = 16 }$.
Dividing the Sum by 2
Now that we have the sum, we can divide it by 2 to find the value of the expression. { \frac{1}{2} (16) = 8 }$.
Substituting the Value
Now that we have the value of the expression, we can substitute it into the original equation. { 12 \cdot m = 8 }$.
Solving for { m $}$
To solve for { m $}$, we need to isolate the variable. We can do this by dividing both sides of the equation by 12.
Dividing Both Sides by 12
{ \frac{12 \cdot m}{12} = \frac{8}{12} }$.
Simplifying the Equation
The equation can be simplified by canceling out the 12 on the left-hand side. { m = \frac{8}{12} }$.
Reducing the Fraction
The fraction { \frac{8}{12} }$ can be reduced by dividing both the numerator and the denominator by their greatest common divisor, which is 4.
Reducing the Fraction
{ \frac{8}{12} = \frac{2}{3} }$.
Conclusion
In conclusion, the value of { m $}$ is { \frac{2}{3} }$. This is the solution to the equation { 12 \cdot m = \frac{1}{2} (6, 10) }$.
Introduction
In our previous article, we solved for { m $}$ in the equation { 12 \cdot m = \frac{1}{2} (6, 10) }$. In this article, we'll answer some frequently asked questions related to solving for { m $}$.
Q: What is the value of { m $}$ in the equation { 12 \cdot m = \frac{1}{2} (6, 10) }$?
A: The value of { m $}$ is { \frac{2}{3} }$.
Q: How do I simplify the expression { \frac{1}{2} (6, 10) }$?
A: To simplify the expression { \frac{1}{2} (6, 10) }$, you need to add 6 and 10, and then divide the result by 2.
Q: What is the order of operations for evaluating the expression { \frac{1}{2} (6, 10) }$?
A: The order of operations for evaluating the expression { \frac{1}{2} (6, 10) }$ is:
- Add 6 and 10
- Divide the result by 2
Q: How do I solve for { m $}$ in the equation { 12 \cdot m = \frac{1}{2} (6, 10) }$?
A: To solve for { m $}$ in the equation { 12 \cdot m = \frac{1}{2} (6, 10) }$, you need to:
- Evaluate the expression { \frac{1}{2} (6, 10) }$
- Substitute the value into the equation
- Divide both sides of the equation by 12
Q: What is the greatest common divisor of 8 and 12?
A: The greatest common divisor of 8 and 12 is 4.
Q: How do I reduce the fraction { \frac{8}{12} }$?
A: To reduce the fraction { \frac{8}{12} }$, you need to divide both the numerator and the denominator by their greatest common divisor, which is 4.
Q: What is the reduced fraction of { \frac{8}{12} }$?
A: The reduced fraction of { \frac{8}{12} }$ is { \frac{2}{3} }$.
Conclusion
In conclusion, we've answered some frequently asked questions related to solving for { m $}$ in the equation { 12 \cdot m = \frac{1}{2} (6, 10) }$. We hope this article has been helpful in understanding the solution to the equation.
Additional Resources
If you're looking for more information on solving for { m $}$, we recommend checking out the following resources:
Contact Us
If you have any further questions or need additional help, please don't hesitate to contact us. We're here to help!