The sum and product of two numbers are 11 and 18 respectively. Then the sum of…

Concept

For two non-zero numbers x and y, reciprocal fractions are added by using the common denominator xy. Therefore 1/x + 1/y = (x+y)/(xy): the numerator is the original sum and the denominator is the original product.

Application

1. Let the numbers be x and y. The given conditions are x + y = 11 and xy = 18.

2. Write the requested sum: 1/x + 1/y.

3. Use the common denominator xy: 1/x + 1/y = (y+x)/(xy) = (x+y)/(xy).

4. Substitute the given sum and product: (x+y)/(xy) = 11/18.

Cross-check

The numbers can be 2 and 9 because 2 + 9 = 11 and 2 × 9 = 18. Their reciprocals give 1/2 + 1/9 = (9+2)/18 = 11/18, confirming the calculation independently.

Result

Hence, the sum of the reciprocals is 11/18.