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