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The additive inverse of a number is the negative of that number.

Given one number, its additive inverse is the number that needs to be added to it so that the sum is zero.

Thus:

The additive inverse of 2.5 is -2.5

The additive inverse of -7.998 is 7.998

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โˆ™ 2010-09-29 11:16:00
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A polynomial of degree zero is a constant term

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Q: What does mean additive inverses?
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Are two integers that are opposite also called additive inverses.?

Yes. Those would be numbers such as 5 and -5, which only have opposite signs - they are called additive inverses (of one another).


What is the difference between the zero property of multiplication and the identity property of addition?

Usually, the identity of addition property is defined to be an axiom (which only specifies the existence of zero, not uniqueness), and the zero property of multiplication is a consequence of existence of zero, existence of an additive inverse, distributivity of multiplication over addition and associativity of addition. Proof of 0 * a = 0: 0 * a = (0 + 0) * a [additive identity] 0 * a = 0 * a + 0 * a [distributivity of multiplication over addition] 0 * a + (-(0 * a)) = (0 * a + 0 * a) + (-(0 * a)) [existence of additive inverse] 0 = (0 * a + 0 * a) + (-(0 * a)) [property of additive inverses] 0 = 0 * a + (0 * a + (-(0 * a))) [associativity of addition] 0 = 0 * a + 0 [property of additive inverses] 0 = 0 * a [additive identity] A similar proof works for a * 0 = 0 (with the other distributive law if commutativity of multiplication is not assumed).


What is the additive of -4?

If you mean the ADDITIVE INVERSE, change the minus sign to a plus sign. (And if you see a plus sign, you change it to a minus sign.)


Are additive inverses the same as opposites?

The opposite is defined in the context of an operation. So, if the operation is addition, then the opposite is the additive inverse. If the operation in multiplication, then the opposite is the reciprocal. If the operation is exponentiation then the opposite is the logarithm, if the operation is sine then the opposite is arc sine. In function notation, if y = f(x) then the opposite is x = f-1(y), which may or may not always be defined.


What is the sum of any number and its opposite?

I assume you mean the additive inverse. The sum of any number and its additive inverse is zero. For example, 7 + (-7) = 0.

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