Question

$\frac{27}{x} + \frac{47}{y} = 110$
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Answer 1

Answer:

Mainly it's a difference of size:

\dfrac means that the fraction is set in displaystyle

\tfrac means that the fraction is set in textstyle

with \frac: the actual context implies the decision above

For example, if you have a complicated mathematical expression in the middle of some array environment (which, by default, employs text-style math), you can use \dfrac to force the use of displaystyle math mode for the fraction

\dfrac and \tfrac are from the amsmath package

Aside: TeX provides four math "styles": display style, text style, script style, and scriptscript style. scriptstyle is generally meant for level-1 subscripts and superscripts, and scriptscriptstyle is for level-2 subscripts and superscripts.