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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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