Question

What is the additive inverse of \[ - \left( {\dfrac{{ - 2}}{3}} \right)\] ?

Answer 1

Hint: The value of an additive inverse of a number is defined as the value that when added to the original number yields zero. It's the amount we add to a number to make it equal zero. If an is the original number, then its additive inverse is minus a, or –a.

Complete step by step solution:
By simplifying \[ - \left( {\dfrac{{ - 2}}{3}} \right)\] we get,
\[ - \left( {\dfrac{{ - 2}}{3}} \right) = \dfrac{2}{3}\] ...... \[\left[ {\because \left\{ {\left( - \right) + \left( - \right) = \left( + \right)} \right\}} \right]\]
Now,
\[a + \left( { - a} \right) = a - a = 0\]
Any number's additive inverse, say \[\dfrac{a}{b}\] is \[ - \dfrac{a}{b}\] such that \[\dfrac{a}{b} + \left( {\dfrac{{ - a}}{b}} \right) = 0\].
Therefore according to the above logic ,
To begin, we must multiply the provided number of positive numbers by \[ - 1\] to get
\[\dfrac{{2 \times - 1}}{{3 \times - 1}} = - \dfrac{2}{3}\]
\[\dfrac{2}{3} + \left( {\dfrac{{ - 2}}{3}} \right) = 0\]
Hence , the additive inverse of \[ - \left( {\dfrac{{ - 2}}{3}} \right)\] will be \[\left( {\dfrac{{ - 2}}{3}} \right)\] .
So, the correct answer is “Option B”.

Note: What you add to a number to make the sum zero is called additive inverse. A whole number, a natural number, an integer, a fraction, or any other real number can be used. Assume you have a bucket of room temperature water. You fill it with a litre of hot water, which raises the temperature of the bucket by a specified amount. Add another litre of cold water to the mix now. The different temperatures of water put to the bucket will balance each other out, leaving a bucket of room temperature water.