Simplify the following :$3 \frac{7}{9} + 5 \frac{7}{8} + 1 \frac{23}{24}$

Given :

The given expression is $3 \frac{7}{9} + 5 \frac{7}{8} + 1 \frac{23}{24}$

To do :

We have to simplify the given expression.

Solution :

$3 \frac{7}{9} + 5 \frac{7}{8} + 1 \frac{23}{24}$

Convert mixed fractions into normal fractions, 

$3 \frac{7}{9}  =  \frac{9\times3 +7}{9}  =  \frac{27+7}{9}  =  \frac{34}{9}$

$5 \frac{7}{8}  =  \frac{8\times5 +7}{8}  =  \frac{40+7}{8}  =  \frac{47}{8}$

$1 \frac{23}{24}  =  \frac{24\times1 +23}{24}  =  \frac{24+23}{24}  =  \frac{47}{24}$

now add,   

$\frac{34}{9} +  \frac{47}{8} +  \frac{47}{24}$

Denominators are different, to make them equal, take LCM

LCM of 9 , 8 , 24  is  72

$\frac{34\times8}{9\times8} + \frac{47\times9}{8\times9} + \frac{47\times3}{24\times3}$

$\frac{272}{72} + \frac{423}{72} + \frac{141}{72}$

now the denominators are same,

$\frac{272 + 423 + 141}{72}$

$\frac{836}{72} = 11 \frac{44}{72}$

$3 \frac{7}{9} + 5 \frac{7}{8} + 1 \frac{23}{24} = 11 \frac{44}{72}$

The value of $3 \frac{7}{9} + 5 \frac{7}{8} + 1 \frac{23}{24}$ is $ 11 \frac{44}{72}$

Tutorialspoint

e

Updated on: 10-Oct-2022

30 Views

Kickstart Your Career

Get certified by completing the course

Get Started