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- There is also a property called additive inverse. In additive inverse, we add a certain value to a number (integer) to get zero as the final result. For example, −8+8 = 0 − 8 + 8 = 0 −8 − 8 is an additive inverse of 8 8
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What is additive inverse?
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May 28, 2023 · Definition: Inverse Properties. Inverse Property of Addition for any real number a, \ [a + (−a) = 0\] −a is the additive inverse of a. Inverse Property of Multiplication for any real number a ≠ 0, \ [a \cdot \dfrac {1} {a} = 1\] \ (\dfrac {1} {a}\) is the multiplicative inverse of a.
The additive inverse of a number is the number that, when added to the given number, results in the sum of 0. The additive inverse of a number is also called the opposite or the negation (or negative) of that number.
- The additive inverse of 0 is 0 itself.
- Except for 0, the additive inverse of all other whole numbers (natural numbers) is always negative, since all the natural numbers are positive.
- The sum of a number and its additive identity is the number itself, whereas the sum of a number and its additive inverse is 0.
The additive inverse property is essential in applying the Division and Multiplication Properties of Equality when solving equations. When solving an equation like $3x + 2 = 11$, we can isolate the variable $x$ by subtracting $2$ from both sides, using the additive inverse property: $3x + 2 - 2 = 11 - 2$, which simplifies to $3x = 9$.
- How to Find The Additive inverse?
- Properties
- Additive Inverse of Different Numbers
- Difference Between Additive Inverse and Multiplicative Inverse
The additive inverse of any given number can be found by changing the sign of it. The additive inverse of a positive number will be a negative, whereas the additive inverse of a negative number will be positive. However, there will be no change in the numerical value except the sign. For example, the additive inverse of 8 is -8, whereas the additiv...
Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0. The properties of additive inverse are given below, based on negation of the original number. For example, x is the original number, then its additive inverse is -x. So, here we will see the properties of -x. 1. −(−x) = x ...
We have understood that an additive inverse is added to a value to make it zero. Now this value can be a natural number, integer, rational number, irrational number, complex number, etc. Let us find the additive inverse of different types of numbers.
Additive inverse and multiplicative inverse, both have different properties. See the below table to know the differences.
Properties of Inverse Operations. Inverse Additive Property; The value, which, when added to the original number gives 0, is known as the additive inverse. Suppose, x is the original number, then its additive inverse will be minus of x, i.e., $-$$\text{x}$, such that: $\text{x + ( – x ) = x – x} = 0$ For example, $6+( $ $-$ $ 6)=0$.
- The inverse operation for the square of a number is the square root. If $8^2=64$, then $\sqrt{64}=8$.
- Inverse operations are used to reverse the effect of one operation on the other. The purpose of inverse operations is to understand the relation be...
- The inverse operations are used in solving the equations for isolating the variables by applying inverse operations on both the sides.
There is also a property called additive inverse. In additive inverse, we add a certain value to a number (integer) to get zero as the final result. For example, −8+8 = 0 − 8 + 8 = 0. −8 − 8 is an additive inverse of 8 8. Property 2. In inverse operations multiplication is the inverse of division.
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. When two numbers are added together to get 0, then we say both the numbers are additive inverses of each other.
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