Question

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

\[\frac{2}{- 7} \text{and} \frac{12}{- 35}\]

Answer 1

\[\text{We have}\frac{2}{- 7} \text{and} \frac{12}{- 35} . \]
\[ \therefore \frac{- 2}{7} + \frac{- 12}{35} = \frac{- 2 \times 5}{7 \times 5} + \frac{- 12}{35} = \frac{- 10 - 12}{35} = \frac{- 22}{35}\]
\[\frac{12}{- 35} + \frac{2}{- 7} = \frac{- 12}{35} + \frac{- 2 \times 5}{7 \times 5} = \frac{- 12 - 10}{35} = \frac{- 22}{35}\]
\[ \therefore \frac{2}{- 7} + \frac{12}{- 35} = \frac{12}{- 35} + \frac{2}{- 7}\]
\[\text{Hence verified} . \]