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Jimmy says 3; – 2 is a 4 2 - 1 / 3 What is the actual difference? What did Jimmy do wrong?

Jimmy says 3; – 2 is a 4 2 - 1 / 3 What is the actual difference? What did Jimmy do-example-1
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Given:


3(4)/(9)-2(5)/(6)\text{ is }1(1)/(3)
\begin{gathered} 3(4)/(9)-2(5)/(6)=(31)/(9)-(17)/(6) \\ 3(4)/(9)-2(5)/(6)=(62-51)/(18) \\ 3(4)/(9)-2(5)/(6)=(11)/(18) \end{gathered}
\text{Actual difference is }(11)/(18)

Jimmy done the subtraction directly without changing the mixed fraction to improper fraction and didn't took the LCM.

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