Question

What is the missing numerator in 2 7/9 = 1 _/9 ?

Answer 1

First off, we'll convert the mixed fractions to "improper", and proceed,

$\bf \stackrel{mixed}{2\frac{7}{9}}\implies \cfrac{2\cdot 9+7}{9}\implies \stackrel{improper}{\cfrac{25}{9}} \\\\\\ \stackrel{mixed}{1\frac{x}{9}}\implies \cfrac{1\cdot 9+x}{9}\implies \stackrel{improper}{\cfrac{9+x}{9}}\\\\ -------------------------------\\\\ \cfrac{25}{9}=\cfrac{9+x}{9}\implies 25=9+x\implies 25-9=x\implies 16=x$