How do I solve this fraction addition problem? 4 2 9 + − 9 1 2 yeilds result of − 5 13 18 but WolframAlpha says the answer is − 5 5 18

Question

How do I solve this fraction addition problem?  4      2    9    +  −  9      1    2   yeilds result of   −  5      13    18   but WolframAlpha says the answer is   −  5      5    18

Kiana Cantu · Accepted Answer

In   −  9      1    2    the negative sign applies to the whole quantity. Thus the calculation should be  4      2    9    +  (  −  9      1    2    )  =      38    9    +  (  −      19    2    )  =      76    18    −      171    18    =  −      95    18    =  −  5      5    18

Ryan Robertson · Accepted Answer

In mixed fractions (just as in decimal ones), the sign applies to both whole and fractional parts, so  4      2    9    +  −  9      1    2    =  4      2    9    −      (    9    +          1      2        )    =  (  4  −  9  )  +      (          2      9        −          1      2        )  Since  4  −  9  =  −  5and      2    9    −      1    2    =            2      ×      2              9      ×      2        −            1      ×      9              2      ×      9        =            4      −      9        18    =            −      5        18  the final answer is  −  5  +            −      5        18    =  −      (    5    +          5      18        )    =  −  5      5    18    .

How do I solve this fraction addition problem? 4 2 9 </mfrac> + −

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