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