Additive Inverse
Additive inverse is any number that can bring the overall result to zero. In other words, if a number is added to its additive inverse, the sum of both the numbers becomes zero. For example, if we take the number 3 and add 3 to it, the result is zero. Hence, the additive inverse of 3 is 3.
Even in real life, everything that we see around can be brought to zero if you find the exact inverse of it. For example, the right amount of fire and ice will cancel out each other and the result will be zero. On this page, we are going to learn about the same concept with numbers.
1.  Additive Inverse Property 
2.  Additive Inverse Formula 
3.  Additive Inverse in Algebraic Expressions 
4.  FAQs 
Additive Inverse Property
Additive inverse is what you add to a number to make the sum zero. The number can be a whole number, a natural number, integer, fraction, or any real number. Let’s say you have a bucket of water at room temperature. You add a liter of hot water to it which makes the overall temperature of the bucket rise by a certain amount. Now, add another liter of cold water to it. The contrasting temperatures of water added to the bucket will cancel out each other, and the result will be a bucket of water at room temperature. The same rule applies while finding the additive inverse of a number.
Additive Inverse Formula
The general formula for the additive inverse of a number can be given in the form of a number itself. Any number when added to its negative will cancel out each other and give the overall sum as zero. This is what we do to find out the additive inverse of any given number. Thus, we need to find the negative of that given number. In other words, we need to find –1 × (N). Hence, we can say that :
Additive Inverse of N = –1 × (N)
Additive Inverse in Algebraic Expressions
The property of additive inverse terms can be extended to algebraic expressions. Following the same rule as stated above, the additive inverse of an algebraic inverse is one that makes the sum of all the terms zero. For example, Jimmy had two apples and three peaches. The total number of apples and peaches he had can be represented as 2x + 3y, where 'x' represents the apples and 'y' represents the peaches. He distributed the fruits among his five other friends. Now, the expression can be written as:  x  x  y  y  y, which shows how each fruit was distributed or given away. Therefore, the additive inverse of 2x + 3y is 2x  3y, making the sum of all the elements zero.
Solved Examples on Additive Inverse

Example 1: Simmy has 4 candles in one hand and 7 in another. How many does she need to give away to make her hands empty?
Solution:
Total number of candles that Simmy has: 4+7=11. To make her hands empty, she needs to give away the same number, which is its additive inverse (11+11=0).Therefore, the number of candies that Simmy needs to give away is 11.

Example 2: What is the additive inverse of the expression 13x + 5y  9z?
Solution:
To find the additive inverse of the whole equation, we need to find the additive inverse of each term. For 13x, the additive inverse is 13x, for 5y, the additive inverse is 5y, and for 9z, the additive inverse is +9z.
Therefore, the additive inverse expression becomes: –13x – 5y + 9z.
Practice Questions on Additive Inverse
FAQs on Additive Inverse
What is the Additive Inverse of zero?
Since zero does not have a positive or negative sign associated with it, the additive inverse of zero is zero.
What is the Difference Between Additive Inverse and Multiplicative Inverse?
Additive inverse is what you add to a number to make the sum zero, whereas, the multiplicative inverse is the reciprocal of the given number, which when multiplied together, gives the product as 1.
Does 0 Have an Additive Inverse?
Since zero does not have a positive or negative sign associated with it, the additive inverse of zero is zero.
What is the Additive Inverse of 8?
The additive inverse of 8 is 8. This can be verified as: 8  8 = 0.
What is the Additive Inverse?
Additive inverse is what you add to a number to make the sum zero. For example, the additive inverse of 4 is 4 because their sum is zero.
What is the Additive Inverse of 12?
The additive inverse of 12 is 12. This can be verified by: 12  12 = 0.