We're asked to determine
the multiplicative inverse of negative 12.
The multiplicative inverse of negative 12
is the number we multiply negative 12 by
so that the product is positive one.
So if we write negative 12 as a fraction
with a denominator of one,
we would have negative 12
over positive one times,
and now if we multiply by the reciprocal,
the product will be positive one.
To find the reciprocal of a fraction,
we interchange the
numerator and denominator.
Or we could think of just
flipping the fraction over.
The reciprocal of negative 12 over one
is negative one over 12, or negative 1/12.
Multiplying a negative times
a negative is positive.
The product here is positive
12/12 which is equal to one.
So now we know that negative
12 times negative 1/12
is equal to one, and therefore
the multiplicative inverse
of negative 12 is negative 1/12,
which, again, is a
reciprocal of negative 12.
For the multiplicative
inverse of positive nine,
positive nine as a fraction
would have a denominator of one.
So we have nine over one times,
again, if we multiply by the
reciprocal of nine over one
which is one over nine or 1/9,
multiplying, we have 9/9
which is equal to one.
So now we know that nine
times 1/9 is equal to one,
and therefore the multiplicative inverse
of positive nine is positive 1/9,
which, again, is the reciprocal of nine.
The last example we want to find
the multiplicative inverse of 2/3.
Notice we multiply 2/3 by
its reciprocal which is 3/2.
We get 6/6 which is equal to one,
and therefore the multiplicative
inverse of 2/3 is 3/2.
So again, in general,
the multiplicative
inverse of a given number
is the reciprocal of the given number.
I hope you found this helpful.
