What would the additive and multiplicative inverse of 2 be and how do you solve this?

Answer 1

Alright, here are a few definitions that will help you find the additive and multiplicative inverse of any number!

Additive inverse: The opposite of a given number, n, that when added to n will give 0 as an answer.
Example: What is the additive inverse of 7, 9, 3, -8, -12, and 2?
Answer: -7, -9, -3, 8, 12, and -2.
Reason: 7 + -7 = 0
-8 + 8 = 0
2 + -2 = 0

Multiplicative inverse: The inverse of a given number, n (written as 1/n, or n^-1), that when multiplied by n gives 1 as the answer.
Example: 2, 4, -6, -8
Answer: 1/2, 1/4, -1/6, -1/8
Reason: 2 * (1/2) = 1
4 * (1/4) = 1
-8 * (-1/8) = 1

There you go! Now you can easily calculate the inverses of any given number! Hope this helps :)

Answer 2

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BearMember since: August 22, 2007
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additive inverse means the value that added to it equals 0
thus that would be -2

multiplicative inverse means the value multiplied to it that equals 1, thus that would be 1/2

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murnipMember since: August 21, 2006
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murnip
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Additive inverse is -2
Multiplicative inverse is 1/2

You get the additive inverse of a number by multiplying it by
-1.
You get the multiplicative inverse of a number by dividing 1 by the number.

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by murnip
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steppy333Member since: September 05, 2007
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To find an inverse of a number, you first need to decide what the identity is, for that operation.

Considering addition, what number x satisfies the following:

a + x = a.

Clearly its 0, so the identity is 0.

Considering multiplication, what number x satisfies the following:

ax = a

The answer is 1, so the identity is 1.

Now, the inverse x of a number a is s.t

a * x = e, ... ... where * is the operation (addition, multiplication...) and e is the identity.

So, for addition,

a + x = 0

The inverse x will be -a.

For multiplication,

ax = 1

The inverse x will be 1/a.

Since in your question a = 2, the additive inverse is -2 and the multiplicative inverse is 1/2.

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by steppy333
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gjmb1960Member since: July 08, 2006
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it depends in what ring.

in N ,2 doesnt have an additive inverse, in Z the additive inverse of 2 is -2, in Z/3 it is 1

multiplicative idem dito
in N, Z none, in Q it is 1/2 , in Z/3 it is 2 itself.

greetings.

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