Subtraction
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The number (-9) is the additive inverse of 9.Inverse operations can also be used to find the additive inverse of a specific number. For example, -9 is the additive inverse of 9 since the sum of -9 and 9 is 0. Additive inverses come in pairs; 9 is the additive inverse of -9, just as -9 is the additive inverse of 9. Any two numbers are additive inverses if they add up to 0.Visualize a pair of additive inverses on the number line. The number 9 and its additive inverse -9 are both nine units away from 0 but on opposite sides of 0. For this reason, -9 is called the opposite of 9, and 9 is the opposite of -9. The opposite of a number may be positive or negative.
We are talking group theory here. A group with addition has an additive inverse. A group with multiplication has a multiplicative inverse. The additive inverse of a number x is a y with x + y = 0. The additive inverse of x is written -x. Hence, the additive inverse of 9.1 equals -9.1. The reason that this question can arise is that beyond groups, there are rings and fields. Rings and fields have, besides addition, also multiplication. An element can have an additive inverse and a multiplicative inverse at the same time.
The "additive inverse" is essentially the negative value. It changes the number in the opposite direction on a number line. If you add a number to a value, and then add its inverse, you will have the same original value.Example: 2 + 3 = 5 , then 5 + (-3) = 2---The "multiplicative inverse" is the reciprocal of a number (i.e. for x, it is 1/x )Dividing by a number (especially a fraction) can be done by multiplying its inverse.Examples:The division 6 divided by 2 = 3 is the same as 6 times its inverse (1/2), also 3.The division 9 divided by 3/4 is the same as 9 x 4/3 = 36/3 = 12
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additive inverse and associative property and if one is involved, then also identity