Answer:
A fraction with a denominator of \(4\) that is less than \(\frac{7}{12}\)miles is \(\frac{1}{4}\).
Step-by-step explanation:
Let the fraction be
\(\frac{x}{4}\)
Since this fraction must be less than \(\frac{7}{12}\) miles, we can write the inequality,
\(\frac{x}{4}\:<\:\frac{7}{12}\)
We now solve the inequality for \(x\) to obtain,
\(x\:<\:\frac{7}{12}\times 4\)
This simplifies to,
\(x\:<\:\frac{7}{3}\)
This implies that,
\(x\:<\:2\frac{1}{3}\)
This is distance so \(x\) must be positive.
So we can choose \(x=1\) or \(x=2\).
Therefore the possible fractions include \(\frac{1}{4}\) or \(\frac{2}{4}\).
In the simplest form, the most appropriate fraction is \(\frac{1}{4}\)
