Question

How do you divide fractions with different denominators with whole numbers?

Answer 1

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

`\bf \begin{cases} 7(3)/(4)\implies \cfrac{7\cdot 4+3}{4}\implies &\cfrac{31}{4} \\\\ 2(2)/(9)\implies \cfrac{2\cdot 9+2}{9}\implies &\cfrac{20}{9} \end{cases}\\\\ -----------------------------\\\\ thus\qquad \cfrac{7(3)/(4)}{2(2)/(9)}\implies \cfrac{(31)/(4)}{(20)/(9)}\\\\ -----------------------------\\\\ recall\implies \cfrac{(a)/(b)}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\qquad then\\\\ -----------------------------\\\\`


`\bf \cfrac{(31)/(4)}{(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(39)/(80)}\impliedby \cfrac{3\cdot 80+39}{80}\implies \cfrac{279}{80}`