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.

Given:

Portion of cake given to Naina $=1\frac{1}{2}$

Portion of cake given to Najma $=1\frac{1}{3}$

To do: 

We have to find the total portion of cake given to Naina and Najma.

Solution: 

The total portion of the cake given to Naina and Nagma 
$=$

Portion of cake given to Naina $+$ Portion of cake given to Najma

$=1\frac{1}{2} \ +\ 1\frac{1}{3}$

$=\frac{1\times2+1}{2}+\frac{1\times3+1}{3}$

$=\frac{3}{2} \ +\ \frac{4}{3}$

LCM of 3 and 2 is 6:

Therefore,

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

$=\frac{9\ +\ 8}{6}$

$=\frac{17}{6}$

$=\frac{2\times6+5}{6}$

$=\mathbf{2\frac{5}{6}}$

Therefore, the total portion of cake given to both Naina and Najma is $2\frac{5}{6}$.

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Updated on: 10-Oct-2022

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