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Properties of Rational Numbers - Additive Inverse of Rational Number

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Additive Inverse of Rational Number:

`(- 5)/7 "must be multiplied by" 7/(- 5)` so as to get the product 1.

`7/(- 5) "is the reciprocal of" (- 5)/7`.

`7/-5 xx -5/7 = 1`.

The reciprocal or multiplicative inverse of  another non-zero rational number `a/b` if ` a/b xx c/d = 1`.

Example

Write the additive inverse of the following: `(-7)/19`

`7/19 "is the additive inverse of" (- 7)/19 "because" (- 7)/19 + 7/(19) = (- 7 + 7)/19 = 0/19 = 0.`

Example

Write the additive inverse of the following:  `21/112`.

The additive inverse of `(21)/(112) "is" (-21)/112`.

Example

Verify that – (-x) is the same as x for `"x" = 13/17`.

x = `13/17`

The additive inverse of x = `13/17  "is" - x = (-13)/17 "since" 13/17 + ((-13)/17) = 0.`
The same equality `13/17 + ((-13)/17) = 0`,
shows that the additive inverse of `(-13)/17  "is"  13/17 "or" -((-13)/17) = 13/17` i.e., -(- x) = x.

Example

Verify that – (-x) is the same as x for `x = (-21)/31`.

Additive inverse of `"x" = (-21)/31 "is -x" = 21/31 "since" (-21)/31 + 21/31 = 0.`

The same equality `(-21)/31 + 21/31 = 0,`

shows that the addiditive inverse of `21/31 "is" (-21)/31, i.e., -(-x) = x`.

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