Question

Evaluate:
$\frac{-9}{4}+\frac{13}{3}+\frac{25}{6}$

Answer 1

Step 1: Finding LCM of denominators of given numbers

Given, numbers $\frac{-9}{4},\frac{13}{3},\frac{25}{6}$
$\therefore LCM\text{of}4,3\text{and}6=3\times 2\times 2\times 1\times 1=12.$

Step: 2 Making the denominators of the rational number equal to LCM i.e. 12
To make the denominators equal to 12 we have to multiply and divide the first fraction by 3 second by 4 and third by 2.
$\frac{-9\times 3}{4\times 3}=\frac{-27}{12}$
$\frac{13\times 4}{3\times 4}=\frac{52}{12}$
$\frac{25\times 2}{6\times 2}=\frac{50}{12}$

Step 3: Adding $\frac{-27}{12},\frac{52}{12}$ and $\frac{50}{12}$
Since, denominators are same i.e. 12, hence add the numerators.
$\frac{-27}{12}+\frac{52}{12}+\frac{50}{12}$
$=\frac{-27+52+50}{12}$
$[\because$ denominators are same, only adding the numerators ]
$\frac{25+50}{12}$
$\frac{75}{12}$
$=\frac{75÷3}{12÷3}$
$=\frac{25}{4}$
Hence, the required answer is $\frac{25}{4}.$