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Using commutativity and associativity of addition of rational numbers, express the following as a rational number: $\frac{4}{7} + 0 + \frac{(- 8)}{9} + \frac{(- 13)}{7} + \frac{17}{21} .$

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\frac{(- 86)}{63}

\frac{63}{85}

\frac{63}{(- 86)}

\frac{86}{63}

answer is A.

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Detailed Solution

Given,

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

Grouping the numbers having same denominator, as commutative property of addition is,

a + b = b + a

Therefore,

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

LCM of 9 and 21 is 63, then simplify

\Rightarrow (\frac{4 - 13}{7}) + (\frac{- 56 + 51}{63})

\Rightarrow \frac{(- 9)}{7} + \frac{(- 5)}{63}

Taking LCM and simplify,
LCM of 7 and 63 is 441.

\Rightarrow \frac{- 567 - 35}{441}

(\frac{a \times d + b \times c}{b \times d})

\Rightarrow \frac{(- 602)}{441}

\Rightarrow \frac{(- 86)}{63}

Therefore, the required answer is

\frac{(- 86)}{63}

.
Correct option is 1.

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