<s>[INST] How do I solve this fraction addition problem? $4\frac{2}{9} + -9\frac{1}{2}$ yeilds result of $-5\frac{13}{18}$ but WolframAlpha says the answer is $-5\frac{5}{18}$
fixed.
 [/INST] In mixed fractions (just as in decimal ones), the sign applies to both whole and fractional parts, so
$$4\frac{2}{9} + -9\frac{1}{2}=4\frac{2}{9}-\left(9+\frac{1}{2}\right)=(4-9)+\left(\frac{2}{9}-\frac{1}{2}\right)$$
Since
$$4-9=-5$$
and
$$\frac{2}{9}-\frac{1}{2}=\frac{2\times2}{9\times2}-\frac{1\times9}{2\times9}=\frac{4-9}{18}=\frac{-5}{18}$$
the final answer is
$$-5+\frac{-5}{18}=-\left(5+\frac{5}{18}\right)=-5\frac{5}{18}.$$
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