The sum of a number and its reciprocal is 3 29/52.
Using formal algebra....
let the number be x; then the reciprocal is 1/x
3 29/52 = (156+29)/52 = 185/52
Try factoring that; or use the quadratic formula....
It does in fact factor:
or
ANSWER: The number and its reciprocal are, in either order, 4/13 and 13/4
The answer can be obtained far more easily using logical reasoning, simple trial and error, and easy arithmetic.
(1) Since the sum is a bit more than 3, the larger number must be a bit more than 3.
(2) Since the denominator of the sum is 52, the most likely denominators of the two fractions x and 1/x are 13 and 4.
So try 13/4 and 4/13 for the two numbers and verify that their sum is indeed 3 29/52.
