Question

Naina was given $1\frac{1}{2}$ piece of cake and Najma was given $1\frac{1}{3}$ piece of cake. Find the total amount of cake was given to both of them.

Answer 1

Determine the total amount of cake given to both Naina and Najma.

The fraction of cake given to Naina is $1\frac{1}{2}=\frac{3}{2}$.

The fraction of cake given to Najma is $1\frac{1}{3}=\frac{4}{3}$.

$\begin{array}{rcl}\mathrm{Total}\mathrm{amount}\mathrm{of}\mathrm{cake}\mathrm{given}\mathrm{to}\mathrm{both}\mathrm{of}\mathrm{them}& =& \frac{3}{2}+\frac{4}{3}\\ & =& \frac{3\times 3}{2\times 3}+\frac{4\times 2}{3\times 2}[\mathrm{Converting}\mathrm{unlike}\mathrm{fractions}\mathrm{to}\mathrm{like}\mathrm{fractions},\mathrm{LCM}\mathrm{of}2\mathrm{and}3\mathrm{is}6]\\ & =& \frac{9}{6}+\frac{8}{6}\\ & =& \frac{9+8}{6}\\ & =& \frac{17}{6}\\ & =& 2\frac{5}{6}\end{array}$

Hence, both of them were given $2\frac{5}{6}$ pieces of cake.