Respuesta :
first off, you make the mixed fraction with only 1 numerator and one denominator, a mixed fraction will end up with a numerator bigger than the numerator, because, it has several whole, in the case of 7 3/4, it has 7 wholes, anyhow, a fraction with a bigger numerator than denominator is so-called an "improper fraction".
anyhow... you'd multiply the whole times the denominator, and add the numerator, and that's the new numerator
let us divide those
[tex]\bf \begin{cases} 7\frac{3}{4}\implies \cfrac{7\cdot 4+3}{4}\implies &\cfrac{31}{4} \\\\ 2\frac{2}{9}\implies \cfrac{2\cdot 9+2}{9}\implies &\cfrac{20}{9} \end{cases}\\\\ -----------------------------\\\\ thus\qquad \cfrac{7\frac{3}{4}}{2\frac{2}{9}}\implies \cfrac{\frac{31}{4}}{\frac{20}{9}}\\\\ -----------------------------\\\\ recall\implies \cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\qquad then\\\\ -----------------------------\\\\ [/tex]
[tex]\bf \cfrac{\frac{31}{4}}{\frac{20}{9}}\implies \cfrac{31}{4}\cdot \cfrac{9}{20}\implies \cfrac{31\cdot 9}{4\cdot 20}\implies \boxed{\cfrac{279}{80}} \\\\\\\\ \boxed{3\frac{39}{80}}\impliedby \cfrac{3\cdot 80+39}{80}\implies \cfrac{279}{80} [/tex]
anyhow... you'd multiply the whole times the denominator, and add the numerator, and that's the new numerator
let us divide those
[tex]\bf \begin{cases} 7\frac{3}{4}\implies \cfrac{7\cdot 4+3}{4}\implies &\cfrac{31}{4} \\\\ 2\frac{2}{9}\implies \cfrac{2\cdot 9+2}{9}\implies &\cfrac{20}{9} \end{cases}\\\\ -----------------------------\\\\ thus\qquad \cfrac{7\frac{3}{4}}{2\frac{2}{9}}\implies \cfrac{\frac{31}{4}}{\frac{20}{9}}\\\\ -----------------------------\\\\ recall\implies \cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\qquad then\\\\ -----------------------------\\\\ [/tex]
[tex]\bf \cfrac{\frac{31}{4}}{\frac{20}{9}}\implies \cfrac{31}{4}\cdot \cfrac{9}{20}\implies \cfrac{31\cdot 9}{4\cdot 20}\implies \boxed{\cfrac{279}{80}} \\\\\\\\ \boxed{3\frac{39}{80}}\impliedby \cfrac{3\cdot 80+39}{80}\implies \cfrac{279}{80} [/tex]
