Question

Add the following rational numbers:

\[\frac{- 7}{27} and \frac{11}{18}\]

Answer 1

\[\text{The L.C.M. of denominators 27 and 18 is 54} . \]
\[\text{Now, we will express} \frac{- 7}{27} \text{and} \frac{11}{18} \text{in the form in which they take the denominator 54} . \]
\[\frac{- 7 \times 2}{27 \times 2} = \frac{- 14}{54} \]
\[\frac{11 \times 3}{18 \times 3} = \frac{33}{54}\]
\[\frac{- 7}{27} + \frac{11}{18} = \frac{- 14}{54} + \frac{33}{54}\]
\[ = \frac{- 14 + 33}{54}\]
\[ = \frac{19}{54}\]