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

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

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Solution

Given $\frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}$

Grouping the given rational numbers with the same denominators together,

$∴ \frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}$
$= 0 + \frac{- 8}{9} + (\frac{4}{7} + \frac{- 13}{7}) + \frac{17}{21}$
$= \frac{- 8}{9} + (\frac{4 - 13}{7}) + \frac{17}{21}$
$= \frac{- 8}{9} + (\frac{- 9}{7}) + \frac{17}{21}$
$= \frac{- 8}{9} + \frac{- 9 \times 3}{7 \times 3} + \frac{17}{21}$
$= \frac{- 8}{9} + \frac{- 27}{21} + \frac{17}{21}$
$= \frac{- 8}{9} + \frac{- 10}{21}$
$= \frac{- 8 \times 7}{9 \times 7} + \frac{- 10 \times 3}{21 \times 3}$
$= \frac{- 56}{63} + \frac{- 30}{63}$
$= \frac{- 86}{63}$

Hence, $\frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21} = \frac{- 86}{63}$

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

Q. 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) $- 4 a n d \frac{4}{- 7}$