Question Video: Finding the Additive Inverse of a Fraction | Nagwa Question Video: Finding the Additive Inverse of a Fraction | Nagwa

# Question Video: Finding the Additive Inverse of a Fraction Mathematics • First Year of Preparatory School

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Find the additive inverse of −1/3.

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### Video Transcript

Find the additive inverse of negative one-third.

In this question, we are asked to find the additive inverse of a given rational number. To do this, we can start by recalling that the additive inverse of a number 𝑎 is the number whose sum with 𝑎 gives zero, which is the additive identity.

We can find the additive inverse of any number by recalling that 𝑎 plus negative 𝑎 is always equal to zero. In particular, this means that negative 𝑎 is the additive inverse of 𝑎 for any rational number 𝑎. Hence, the additive inverse of negative one-third is negative one times negative one-third. Since the product of two negatives is positive, this is equal to one-third.

We can verify that these numbers are additive inverses by calculating that negative one-third plus one-third is equal to zero. This confirms that one-third is the additive inverse of negative one-third.

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