# 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.

#### Complete Python Prime Pack for 2023

9 Courses     2 eBooks

#### Artificial Intelligence & Machine Learning Prime Pack

6 Courses     1 eBooks

#### Java Prime Pack 2023

8 Courses     2 eBooks

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 $2\frac{5}{6}$.

Updated on 10-Oct-2022 13:33:02