Question

Verify commutativty of addition of rational numbers for each of the following pairs of rotional numbers: 

\[- 4\ \text{and} \frac{4}{- 7}\]

Answer 1

\[\text{We have - 4 and} \frac{4}{- 7} . \]
\[ \therefore \frac{- 4}{1} + \frac{- 4}{7} = \frac{- 4 \times 7}{1 \times 7} + \frac{- 4}{7} = \frac{- 28 - 4}{7} = \frac{- 32}{7}\]
\[ \frac{- 4}{7} + \frac{- 4}{1} = \frac{- 4}{7} + \frac{- 4 \times 7}{1 \times 7} = \frac{- 4 - 28}{7} = \frac{- 32}{7}\]
\[ \therefore - 4 + \frac{4}{- 7} = \frac{4}{- 7} - 4\]
\[ \text{Hence verified} . \]