Question

A length a ribbon is 3 1/2 yard how many pieces at 1 5/9

Answer 1

Namely, how many times does 1 and 5/9 go into 3 1/2

let's first convert the mixed fractions to "improper", then divide then.

$\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} \\\\\\ \stackrel{mixed}{1\frac{5}{9}}\implies \cfrac{1\cdot 9+5}{9}\implies \stackrel{improper}{\cfrac{14}{9}}\\\\ -------------------------------\\\\ \cfrac{\quad\frac{7}{2} \quad }{\frac{14}{9}}\implies \cfrac{7}{2}\cdot \cfrac{9}{14}\implies \cfrac{7\cdot 9}{2\cdot 14}\implies \cfrac{63}{28}\implies \cfrac{9}{4}\implies 2\frac{1}{4}$