Question

Ryan claims that any fraction located between 1/5 and 1/3 on a number line must have a denominator of 4. Enter a fraction that shows Ryan's Claim is incorrect.

Answer 1

let's firstly convert both fractions with the same denominator, by simply multiplying one by the denominator of the other, let's proceed,

$\bf \cfrac{1}{5}\cdot \cfrac{3}{3}\implies \cfrac{3}{15}~\hspace{7em}\cfrac{1}{3}\cdot \cfrac{5}{5}\implies \cfrac{5}{15} \\\\[-0.35em] ~\dotfill\\\\ \boxed{\cfrac{3}{15}}\rule[0.35em]{10em}{0.25pt}~~\cfrac{4}{15}~~\rule[0.35em]{10em}{0.25pt}\boxed{\cfrac{5}{15}}$

well, low and behold, 4/15 doesn't simplify further and is right between those two, and its denominator is not 4.