- Identify the given equation \(\frac{v}{4} = 4\).
- Isolate the variable \(v\) by multiplying both sides of the equation by 4.
- Calculate the result: \(v = 4 \times 4 = 16\).
- Final answer: \(\boxed{16}\).
Explanation
- Problem Analysis
We are given the equation \(\frac{v}{4} = 4\). Our goal is to solve for the variable \(v\). The equation shows that \(v\) is being divided by 4, and the result of this division is 4. To isolate \(v\), we need to reverse this operation.
- Solving for v
The inverse operation of division by 4 is multiplication by 4. To maintain the equality of the equation, we must apply this operation to both sides:
\[4 \times \left(\frac{v}{4}\right) = 4 \times 4\]
By simplifying the left side, the 4 in the numerator and the 4 in the denominator cancel out, leaving just \(v\):
\[v = 4 \times 4\]
\[v = 16\]
Examples
Imagine you have a box of cookies that you want to share equally among 4 friends. If each friend receives 4 cookies, how many cookies were in the box originally? This problem can be modeled by the equation \(\frac{v}{4} = 4\), where \(v\) represents the total number of cookies. By multiplying the number of friends by the cookies each received, you find the total, which is \(\boxed{16}\). This simple algebraic concept helps in daily tasks like scaling recipes, budgeting, or planning resources.