Question

Add the following rational numbers:

\[\frac{31}{- 4} and \frac{- 5}{8}\]

Answer 1

\[\text{We have} \]
\[\frac{31}{- 4} + \frac{- 5}{8} = \frac{- 31}{4} + \frac{- 5}{8}\]
\[\text{The L.C.M. of denominators 4 and 8 is 8} . \]
\[\text{Now, we will express} \frac{- 31}{4} \text{in the form in which it takes the denominator 8}+ . \]
\[\frac{- 31 \times 2}{4 \times 2} = \frac{- 62}{8}\]
\[\text{So}\]
\[\frac{- 31}{4} + \frac{- 5}{8} = \frac{- 62}{8} + \frac{- 5}{8}\]
\[ = \frac{( - 62) + ( - 5)}{8}\]
\[ = \frac{- 62 - 5}{8}\]
\[ = \frac{- 67}{8}\]