Additive Inverse


 
 
Concept Explanation
 

Additive Inverse

Additive Inverse Of A Rational Number :

The opposite, or additive inverse, of a number is the same distance from 0 on a number line as the original number, but on the other side of 0. Zero is its own additive inverse. In other words, the additive inverse of a rational number is the same number with opposite sign. For example additive inverse of 2/3 is -2/3.

For every rational number frac{a}{b}  there is a rational number frac{c}{d}  such that: frac{a}{b}+frac{c}{d}=0=frac{c}{d}+frac{a}{b}

The rational numbers frac{a}{b};and;frac{c}{d}  satisfying the above property are called additive inverse or negative of each other. The additive inverse of    frac{a}{b}  is written as -frac{a}{b}.

Illustration: Write the additive inverse of each of the following rational numbers:

(i);frac{4}{9} (ii);frac{-13}{7} (iii);frac{5}{-11} (iv);frac{-11}{-14}

Solution:The additive inverse can be written as:

(i)  The additive inverse of  frac{4}{9}  is  -left(frac{-4}{9}right)=frac{-4}{9}

(ii) The additive inverse of  frac{-13}{7} is -left ( frac{-13}{7} right )=frac{13}{7}

(iii) We have,  frac{5}{-11}=frac{-5}{11} . The additive inverse of frac{-5}{11}  is  -left ( frac{-5}{11} right )=frac{5}{11}

(iv) We have,  frac{-11}{-14}=frac{11}{14}.  The additive inverse of  frac{11}{14} is -left ( frac{11}{14} right )=frac{-11}{14}

Illustration: Add the rational number frac{2}{3} and its additive inverse.

Solution :  The additive inverse of frac{2}{3} is -frac{2}{3}

Then, we have to add the number with the additive inverse

frac{2}{3}+left(-frac{2}{3}right)

Rightarrow frac{2}{3}-left(frac{2}{3}right)=frac{2-2}{3}=frac{0}{3}=0

Sample Questions
(More Questions for each concept available in Login)
Question : 1

The additive inverse large frac{-a}{b} is _______________________

Right Option : A
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Explanation
Question : 2

a + (- a) = 0  is explained by which property?

Right Option : B
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Explanation
Question : 3

The sum of the additive inverse and multiplicative inverse of     large frac{1}{5}   is _____________

Right Option : A
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Explanation
 
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