- Interpret "twenty-five" as \(25\).
- Interpret "is" as the equals sign \(= \).
- Interpret "one-sixth of the number \(n\)" as \(\frac{n}{6}\).
- Assemble these parts to obtain the correct equation: \(\boxed{25 = \frac{n}{6}}\).
Explanation
- Analyzing the Sentence Structure
The problem asks us to translate a sentence into a mathematical equation. The sentence is "twenty-five is one-sixth of the number \(n\)". We break this sentence down phrase by phrase to represent it mathematically:
- "Twenty-five" is represented by the constant \(25\).
- "is" represents the equals sign, \(=\).
- "one-sixth of the number \(n\)" indicates the product of \(1/6\) and \(n\), which is written as \(\frac{1}{6}n\) or \(\frac{n}{6}\).
- Forming and Identifying the Correct Equation
By combining these parts, we form the mathematical equation:
\[25 = \frac{1}{6}n\]
This is equivalent to:
\[25 = \frac{n}{6}\]
Comparing this result to the given options:
- \(25 = \frac{n}{6}\)
- \(25 = 6n\)
- \(6 = 25n\)
- \(\frac{1}{6} = \frac{n}{25}\)
The first option matches our derived equation perfectly.
Examples
In real-world applications, mathematical translation is a fundamental skill. For instance, if a recipe calls for a total cooking time where "twenty minutes is one-half of the total time \(T\)", you can quickly translate this into an equation: \(20 = \frac{1}{2}T\). Solving this gives \(T = 40\) minutes, helping you determine how long your meal needs to prepare. This skill allows us to interpret instructions and data efficiently in various daily tasks.