Question

Write the additive inverse of each of the rational number: \[ - \dfrac{{17}}{5}\]

Answer 1

Hint: In the given problem they asked us to find the additive inverse. We know that a rational number is a number that can be expressed in \[\dfrac{p}{q}\] , here \[q\] is not equal to zero. If \[q\] is equal to zero the number becomes undefined (infinity). We know the definition of an additive inverse is the number needed to bring a negative number to zero.

Complete step-by-step answer:
In general, an additive inverse of a field element \[a\] is an element \[b\] such that \[a + b = b + a = 0\] . Thus only one additive inverse exists for each element. There is no need for subtraction or division. We simply write that additive inverse of \[a\] is \[ - b\] .
For example, the additive inverse of 5 is -5. Because \[5 + ( - 5) = 5 - 5 = 0\]
We can write that the additive inverse of a number is its opposite sign number.
Let’s take the given rational number: \[ - \dfrac{{17}}{5}\] the additive inverse of this number is \[\dfrac{{17}}{5}\] . Because \[ \Rightarrow \dfrac{{17}}{5} + \left( { - \dfrac{{17}}{5}} \right) = \dfrac{{17}}{5} - \dfrac{{17}}{5} = 0\] .
(When we add the given number with the additive inverse of that number it will give us zero.)
So, the correct answer is “\[\dfrac{{17}}{5}\]”.

Note: They can also ask the multiplicative inverse of the given rational number. For a field element \[a\] not equal to 0 a multiplicative inverse of \[a\] is an element \[b\] such that \[a.b = b.a = 1\] thus only one multiplicative inverse exists for each element. That is the multiplicative inverse of \[ - \dfrac{{17}}{5}\] is \[ - \dfrac{5}{{17}}\] . This is because \[ - \dfrac{{17}}{5} \times - \dfrac{5}{{17}} = 1\] . The multiplicative inverse of 2 is \[\dfrac{1}{2}\] . That is just taking the inverse of a given number. Remember that the multiplicative inverse sign of a number doesn't change.