The additive inverse of a number is what you can add to that number for the sum to be zero. For real numbers, such as rational numbers, that means the additive inverse can be found by just flipping the sign of the number.
The additive inverse property says if you add a number and its additive inverse, then the sum is zero.
For example, let's use the number 3. The additive inverse of 3 is -3, since 3 + (-3) = 0. This is also true the other way around. The additive inverse of -3 is 3.
When subtracting rational numbers, remember that subtracting is the same as adding a negative! That means 3 - 3 is the same as 3 + (-3) or -3 - (-3) is the same as -3 + 3. Both of these sums involve a number and its additive inverse and they add up to zero.
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For the problem, I don't think you gave me the complete problem, or perhaps there's a typo? Let me know and then I can edit my response to help you out :)
