- Identify the linear equation \(\frac{n}{8} = 3\).
- Multiply both sides by 8 to isolate the variable \(n\).
- Calculate the resulting product: \(3 \times 8 = 24\).
- State the final answer: \(\boxed{24}\).
Explanation
- Analysis of the Equation
The problem provides a linear equation in one variable, \(n\), which is \(\frac{n}{8} = 3\). Our objective is to determine the numerical value of \(n\) that satisfies this equality. This is a straightforward algebraic equation where we need to isolate the variable \(n\) to solve for its value.
- Solving for n
To isolate \(n\), we need to eliminate the divisor 8. We accomplish this by multiplying both sides of the equation by 8. This operation maintains the equality of the equation:
\[\frac{n}{8} \times 8 = 3 \times 8\]
By performing this multiplication, we effectively isolate \(n\) on the left side, leading to:
\[n = 3 \times 8\]
Now, we perform the arithmetic multiplication to find the final value of \(n\):
\[n = 24\]
Examples
Suppose you are baking a batch of cookies and the recipe requires a certain amount of sugar. You know that if you divide your total supply of sugar, represented by \(n\), into 8 equal bowls, each bowl will contain 3 cups. By solving the equation \(\frac{n}{8} = 3\), you can determine that you have \(24\) cups of sugar in total, helping you manage your ingredients efficiently.