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Mathematics

Find the additive inverse of :

(i) 9

(ii) -11

(iii) 813\dfrac{-8}{13}

(iv) 56\dfrac{5}{-6}

(v) 0

Rational Numbers

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Answer

(i) 9

Since, 9 + (-9) = 0

∴ Additive inverse of 9 is -9.

(ii) -11

Since, -11 + 11 = 0

∴ Additive inverse of -11 is 11.

(iii) 813\dfrac{-8}{13}

For a rational number ab\dfrac{a}{b}, the additive inverse is ab\dfrac{-a}{b}.

813\dfrac{-8}{13} + 813\dfrac{8}{13} = 0

∴ Additive inverse of 813\dfrac{-8}{13} is 813\dfrac{8}{13}.

(iv) 56\dfrac{5}{-6}

First, express the number with a positive denominator:

56=5×(1)6×(1)=56\dfrac{5}{-6} = \dfrac{5 \times (-1)}{-6 \times (-1)} = \dfrac{-5}{6}.

Now, find the additive inverse:

56\dfrac{-5}{6} + 56\dfrac{5}{6} = 0

∴ Additive inverse of 56=56\dfrac{5}{-6} = \dfrac{5}{6}.

(v) 0

Zero is its own additive inverse because 0 + 0 = 0.

∴ Additive inverse of 0 is 0.

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