What is additive and multiplicative inverse l
What is additive and multiplicative inverse l
An additive inverse is the number, to a particular number, which will give the additive identity. Likewise, to each number (barring 0 in this case), there is another number, the multiplicative inverse, which will give the multiplicative identity.
Of course to make use of this definition we need to know what an identity is.
An identity of a function is the number that will not induce a change when that function is applied to it.
For example, in relation to the counting numbers, 0 is the additive identity because and number k satisfies the equation k + 0 = k. The multiplicative identity is 1 as for any non-zero number n, n x 1 = n.
to find the additive and multiplicative inverses some simple algebra is all that is required.
the additive inverse of k is:
k + 0 = k
k - k = 0
i.e. k + (-k) = 0
so the additive inverse of k is -k
likewise for multiplication
n x 1 = n
n/n = 1
i.e. n x 1/n = 1
so the multiplicative inverse of n is 1/n.
As the identities and inverses depend on the context of a situation (what function you are using, what set of numbers etc.) it is important to state this before using inverses and additives, especially if doing formal work.
For example, in module 3, the identity would be 3 and the inverse of 1 would be 2.
An additive inverse is the number, to a particular number, which will give the additive identity. Likewise, to each number (barring 0 in this case), there is another number, the multiplicative inverse, which will give the multiplicative identity.
Of course to make use of this definition we need to know what an identity is.
An identity of a function is the number that will not induce a change when that function is applied to it.
For example, in relation to the counting numbers, 0 is the additive identity because and number k satisfies the equation k + 0 = k. The multiplicative identity is 1 as for any non-zero number n, n x 1 = n.
to find the additive and multiplicative inverses some simple algebra is all that is required.
the additive inverse of k is:
k + 0 = k
k - k = 0
i.e. k + (-k) = 0
so the additive inverse of k is -k
likewise for multiplication
n x 1 = n
n/n = 1
i.e. n x 1/n = 1
so the multiplicative inverse of n is 1/n.
As the identities and inverses depend on the context of a situation (what function you are using, what set of numbers etc.) it is important to state this before using inverses and additives, especially if doing formal work.
For example, in module 3, the identity would be 3 and the inverse of 1 would be 2.
