Question

Add and express the sum as a mixed fraction:

\[\frac{- 31}{6} \text{and} \frac{- 27}{8}\]

Answer 1

\[\text{We have}\frac{- 31}{6} + \frac{- 27}{8} . \]
\[\text{L.C.M. of thedenominators 6 and 8 is 24.}\]
\[\text{Now, we will express}\frac{- 31}{6}\text{and}\frac{- 27}{8} \text{in the form in which they take the denominator 24.}\]
\[\frac{- 31 \times 4}{6 \times 4} = \frac{- 124}{24}\]
\[\frac{- 27 \times 3}{8 \times 3} = \frac{- 81}{24}\]
\[ \therefore \frac{- 31}{6} + \frac{- 27}{8} = \frac{- 124}{24} + \frac{- 81}{24}\]
\[ = \frac{- 124 - 81}{24}\]
\[ = \frac{- 205}{24} \]
\[ = - 8\frac{13}{24}\]