Question

Evaluate:
$-\frac{11}{18}+\frac{-3}{9}+\frac{2}{-3}$

Answer 1

Step 1: Finding LCM of denominators of given numbers
Given, Rational numbers:
$-\frac{11}{18},\frac{-3}{9},\frac{2}{-3}i.e.\frac{-11}{18},\frac{-3}{9},\frac{-2}{3}$
$LCM\text{of}3,9,18=3\times 3\times 2=18.$

Step: 2 Making the denominators of the rational number equal to LCM i.e. 18
To make the denominators equal to 18 we have to multiply and divide the second by 2 and third by 6.
$=\frac{-11}{18}$ and
$\frac{-3\times 2}{9\times 2}=\frac{-6}{18}$ and
$\frac{-2\times 6}{3\times 6}=\frac{-12}{18}$

Step 3: Adding $\frac{-11}{18},\frac{-6}{18}$ and $\frac{-12}{18}$
$=\frac{-11}{18}+\frac{-6}{18}+\frac{-12}{18}$
$=\frac{-11+(-6)+(-12)}{18}$
$[\because$ denominators of the rational number are same, hence add the numerators ]
$=\frac{-11-6-12}{18}$
$=\frac{-17-12}{18}$
$=\frac{-29}{18}$
Hence, the required answer is $=\frac{-29}{18}$.