*12 times something equal to 3 is a fraction. To find that value, you would divide 3 by 12, which equals 1/4. So, 12 times 1/4 equals 3.*

Here’s a simple table showing the equation “12 times something equals 3” and the corresponding value for “something”:

Equation | Value of “Something” |
---|---|

12 times something equals 3 | 1/4 |

Equations with unknown variables are the foundation of algebra. Being able to solve for unknowns in equations logically and systematically is a fundamental math skill. In this post, we’ll work through the one-step algebra equation 12 x n = 3 step-by-step to find the value of the unknown n. We’ll also explore key algebra strategies and concepts that are critical for solving more complex algebraic problems. Learning to isolate and solve for unknowns builds algebraic intuition and proficiency.

Understanding the Equation

First let’s interpret what this equation is asking us to do. We have:

12 x n = 3

There is an unknown variable n being multiplied by 12. We don’t know the value of n, but the product of 12 and n equals 3. Our goal is to figure out what single number n could be to make this equation true when multiplied by 12. Let’s recall some algebra rules to help us systematically isolate n.

Algebraic Properties

Here are some key algebra properties we can apply:

- The multiplication property states that if a x b = c, then a = c/b and b = c/a. We can divide both sides by a number to isolate a variable.
- The division property allows us to divide both sides of an equation by the same number, and the equality remains true.
- We can perform the same mathematical operations on both sides of an equation and maintain the equality.

Keeping these in mind, let’s solve our equation step-by-step.

Solving the Equation

12 x n = 3 To isolate n, we divide both sides of the equation by 12 using the division property:

n = 3/12

Using the multiplication fact that 12 x n = 3, we divide both sides by 12 to get n alone on one side.

Simplifying the Solution

The solution n = 3/12 can be simplified by dividing 3 by 12:

n = 3/12 = 1/4

Therefore, the unknown number n must be equal to 1/4 for the original equation 12 x n = 3 to be true.

Checking Our Work

We can verify that we have the right solution by substituting 1/4 back into the original equation:

12 x (1/4) = ? 12 x 0.25 = 3

The equation balances, confirming that n = 1/4 is the correct solution.

Key Takeaways

Let’s summarize some key algebra strategies we demonstrated:

- Use properties like multiplication and division to isolate unknown variables.
- Perform the same steps to both sides of an equation to keep the equality.
- Simplify solutions completely. Write variables in simplest form.
- Check solutions by substituting back into the original equation.
- Break complex problems down into bite-sized steps. Build on algebra fundamentals.
- Practice basic equations regularly to develop skills needed for advanced algebra.

Conclusion

In this post we worked step-by-step through the algebra equation 12 x n = 3 to find the unknown variable n. Explaining each step reinforces the foundational logic and rules of algebra. Building fluency with basic one-variable equations establishes skills to solve more complex mathematical problems. Consistent practice strengthens algebraic thinking and the ability to manipulate unknowns methodically. Every solved equation brings learners one step closer to mastering advanced algebra, unlocking the power of mathematical reasoning to solve real world problems. Keep practicing those equations!

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