Question

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

\[\frac{4}{9} \text{and} \frac{7}{- 12}\]

Answer 1

\[\text{We have}\frac{4}{9} \text{and} \frac{7}{- 12} . \]
\[ \therefore \frac{4}{9} + \frac{- 7}{12} = \frac{4 \times 4}{9 \times 4} + \frac{- 7 \times 3}{12 \times 3} = \frac{16}{36} + \frac{- 21}{36} = \frac{16 - 21}{36} = \frac{- 5}{36}\]
\[\frac{- 7}{12} + \frac{4}{9} = \frac{- 7 \times 3}{12 \times 3} + \frac{4 \times 4}{9 \times 4} = \frac{- 21}{36} + \frac{16}{36} = \frac{- 21 + 16}{36} = \frac{- 5}{36}\]
\[ \therefore \frac{4}{9} + \frac{- 7}{12} = \frac{- 7}{12} + \frac{4}{9}\]
\[ \text{Hence verified} . \]