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Naina was given (1)\(\frac{{1}}{{2}}\) piece of cake and Najma was given (1) \(\frac{{1}}{{3}}\) piece of cake. Findthe total amount of cake was given to both of them.
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Question

Naina was given (1)\(\frac{{1}}{{2}}\) piece of cake and Najma was given (1) \(\frac{{1}}{{3}}\) piece of cake. Findthe total amount of cake was given to both of them.

Answer

amount of cake naina was given = \({1}\frac{{1}}{{2}}={1}+\frac{{1}}{{2}}\)

\(=\frac{{2}}{{2}}+\frac{{1}}{{2}}=\frac{{3}}{{2}}\)

amount of cake najma was given \({1}\frac{{1}}{{3}}={1}+\frac{{1}}{{3}}\)

\(=\frac{{3}}{{3}}+\frac{{1}}{{3}}=\frac{{4}}{{3}}\)

total amount of cake given to both of them = \(\frac{{3}}{{2}}+\frac{{4}}{{3}}\)

\(=\frac{{{3}\cdot{3}}}{{6}}+\frac{{{4}\cdot{2}}}{{6}}\)

\(=\frac{{9}}{{6}}+\frac{{8}}{{6}}=\frac{{{12}+{5}}}{{6}}=\frac{{17}}{{6}}={2}\frac{{5}}{{6}}\)piece

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