Rational Numbers
Additive Inverse
The additive inverse of a number, a, is the number, -a, you add to it to get 0 (the additive identity).
a + (-a) = 0
Examples: The additive inverse of 8 is -8 since 8 + (-8) = 0
The additive inverse of -2 is 2 since -2 + 2 = 0
Multiplicative Inverse
The multiplicative inverse of a number, a, is the number, 1/a, that you multiply it to so you get 1 (the multiplicative identity).
Example: The multiplicative inverse of 5 is 1/5.
The multiplicative inverse of 1/2 is 2.
As integers have additive and multiplicative inverse, similarly, rational numbers also have additive and multiplicative inverse.
Thus, we define additive inverse and multiplicative inverse as:
“If the sum of two rational numbers is 0, then the two rational numbers are said to be additive inverse or negative of each other”.
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“If the multiplication of two numbers gives the result as 1, then the two numbers are called reciprocal or multiplicative inverse of each other”.
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Let us look at some more examples now.
Example 1:
Find the multiplicative inverse of the following rational numbers.
(i) 5/6
(ii) -5/17
(iii) 3/-8
(iv) 
(v) 0.5
Solution:
(i) The multiplicative inverse of 5/6 is 6/5.
(ii) The multiplicative inverse of -15/17 is 17/-15.
(iii) The multiplicative inverse of 3/-8 is-8/3.
(iv)
Thus, the multiplicative inverse of 9/4 is 4/9.
(v) Thus, the multiplicative inverse of 0.5 is 2.
Example 2:
Write the additive inverse of the following rational numbers.
(i) 1/7
(ii) -14/15
(iii) 7/-11
(iv) -2/-5
Solution:
(i) The additive inverse of 1/7 is -1/7.
(ii) The additive inverse of -14/15 is 14/15.
(iii) 
Thus, the additive inverse of 7/-11 is 7/11.
(iv) -2/-5 = 2/5
Thus, the additive inverse of -2/-5 is -2/5.
