pouzdrotf

2022-07-01

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 $-5\frac{5}{18}$

Kiana Cantu

Expert

In $-9\frac{1}{2}$ the negative sign applies to the whole quantity. Thus the calculation should be
$4\frac{2}{9}+\left(-9\frac{1}{2}\right)=\frac{38}{9}+\left(-\frac{19}{2}\right)=\frac{76}{18}-\frac{171}{18}=-\frac{95}{18}=-5\frac{5}{18}$

Ryan Robertson

Expert

In mixed fractions (just as in decimal ones), the sign applies to both whole and fractional parts, so
$4\frac{2}{9}+-9\frac{1}{2}=4\frac{2}{9}-\left(9+\frac{1}{2}\right)=\left(4-9\right)+\left(\frac{2}{9}-\frac{1}{2}\right)$
Since
$4-9=-5$
and
$\frac{2}{9}-\frac{1}{2}=\frac{2×2}{9×2}-\frac{1×9}{2×9}=\frac{4-9}{18}=\frac{-5}{18}$
the final answer is
$-5+\frac{-5}{18}=-\left(5+\frac{5}{18}\right)=-5\frac{5}{18}.$

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