How do I solve this fraction addition problem?

Question

$4\frac{2}{9} + -9\frac{1}{2}$ yeilds result of $-5\frac{13}{18}$ but WolframAlpha says the answer is $-5\frac{5}{18}$

fixed.

Answer 1

TeX \frac directive takes two arguments, but you use three in your formulas. This probably confuses WolframAlpha.

Answer 2

In $-9 \frac12$, the negative sign applies to the whole quantity. Thus the calculation should be

$4 \frac29+(-9 \frac12)=\frac{38}{9}+(-\frac{19}{2})=\frac{76}{18}-\frac{171}{18}=-\frac{95}{18}=-5 \frac{5}{18}$

Answer 3

You can compute $4-9=-5$ and $\frac29-\frac12=\frac4{18}-\frac9{18}=-\frac5{18}$ separately, and then add them up. Or you could compute $4\frac29 + -9\frac12=\frac{38}9-\frac{19}2=\frac{76}{18}-\frac{171}{18}=\frac{-95}{18}=-5\frac5{18}$, though the latter is probably more error prone.

Answer 4

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 $$-5+\frac{-5}{18}=-\left(5+\frac{5}{18}\right)=-5\frac{5}{18}.$$