Question

Add the following rational numbers:

\[\frac{7}{- 18} and \frac{8}{27}\]

Answer 1

\[\frac{7}{- 18} + \frac{8}{27} = \frac{- 7}{18} + \frac{8}{27}\]
\[\text{The L.C.M. of denominators 18 and 27 is 54} . \]
\[\text{Now, we will express} \frac{- 7}{18} \text{and} \frac{8}{27} \text{in the form in which they take the denominator 54} . \]
\[\frac{- 7 \times 3}{18 \times 3} = \frac{- 21}{54} \]
\[\frac{8 \times 2}{27 \times 2} = \frac{16}{54}\]
\[\text{So}\]
\[\frac{- 7}{18} + \frac{8}{27} = \frac{- 21}{54} + \frac{16}{54}\]
\[ = \frac{- 21 + 16}{54}\]
\[ = \frac{- 5}{54}\]
\[ = \frac{- 5}{54}\]