Lan wants to run less than 7/12 miles. It says to find out a fraction with a denominator of 4 and which is less than 7/12.
Let's assume the required fraction to be x/4 such that x/4 is less than 7/12.
[tex] \frac{x}{4} < \frac{7}{12} \\\\
3*\frac{x}{4} < \frac{7}{12}*3 \\\\
\frac{3x}{4} < \frac{21}{12} \\\\
\frac{3x}{4} < \frac{7}{4} \\\\
3x < 7 [/tex]
So we must have multiples of 3's that should be less than 7, we have only two choices 3 < 7 or 6 < 7.
It means x = 1 or x = 2, and the required fraction would be 1/4 or 2/4.
2/4 is simplified to 1/2 and the question says to have denominator 4.
Hence, final answer is 1/4
