Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

ii ) $\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}$

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Solution

Given: $\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}$
Grouping the given rational numbers with the same denominators together,
$∴ \frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9} = (\frac{3}{7} + \frac{- 11}{7}) + (\frac{- 4}{9} + \frac{7}{9})$
$= (\frac{3 - 11}{7}) + (\frac{- 4 + 7}{9})$
$= \frac{- 8}{7} + \frac{3}{9}$
$= \frac{- 8 \times 9}{7 \times 9} + \frac{3 \times 7}{9 \times 7}$
$= \frac{- 72}{63} + \frac{21}{63}$
$= \frac{- 72 + 21}{63}$
$= \frac{- 51}{63}$
$= \frac{- 17}{21}$

Hence, $\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9} = \frac{- 17}{21}$

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Similar questions

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

(i) $\frac{2}{5} + \frac{7}{3} + \frac{- 4}{5} + \frac{- 1}{3}$

(ii) $\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}$

(iii) $\frac{2}{5} + \frac{8}{3} + \frac{- 11}{15} + \frac{4}{5} + \frac{- 2}{3}$

(iv) $\frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}$

Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers: (i) $\frac{- 11}{5} a n d \frac{4}{7}$ (ii) $\frac{4}{9} a n d \frac{7}{- 12}$ (iii) $\frac{- 3}{5} a n d \frac{- 2}{- 15}$ (iv) $\frac{2}{- 7} a n d \frac{12}{- 35}$ (v) $4 a n d \frac{- 3}{5}$ (vi) $- 4 a n d \frac{4}{- 7}$