algebra question

Question

what is the reciprocal of the sum of the reciprocal of -4 and 1/12

Answer 1

Let's start with "reciprocal," which just means that we want to divide 1 by the value. In other words, the reciprocal of x would just be 1 / x.

So we want the reciprocal of "the sum of the reciprocal of -4 and 1/12" ... sounds complicated, but take it one step at a time:

1. The reciprocal of -4 is .... -1/4
2. The sum of the reciprocal of -4 and 1/12 is .... -1/4 + 1/12
3. To add the two fractions we need to use the greatest common denominator, which in this case is 12... (-1/4)*(3/3) + 1/12 = -3/12 + 1/12 = -2/12 = -1/6
4. Now we want the reciprocal of (-1/6), which is just 1 / (-1/6). Using the rules of fraction division we know this must be -6

So: the reciprocal of the sum of the reciprocal of -4 and 1/12 is -6