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

Asked by Sakshi | 1 year ago |  34

1 Answer

Solution :-

Firstly group the rational numbers with same denominators

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

Now the denominators which are same can be added directly.

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

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

\( \dfrac{-9}{7} +\dfrac{ -8}{9} +\dfrac{ 17}{21}\)

By taking LCM for 7, 9 and 21 we get, 63

\(\dfrac{ (-9×9)}{ (7×9)} + \dfrac{(-8×7)}{ (9×7) }+ \dfrac{(17×3)}{ (21×3)}\)

\( \dfrac{-81}{63} + \dfrac{-56}{63} + \dfrac{51}{63}\)

Since the denominators are same can be added directly

\( \dfrac{(-81+(-56)+ 51)}{63 }= \dfrac{(-81-56+51)}{63} = \dfrac{-86}{63}\)

Answered by Aaryan | 1 year ago

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