# Fill in the blanks. (1) Zero has ________ reciprocal. (2) The numbers ________ and ________ are their own reciprocals. (3) The reciprocal of 5 is ________. (4) Reciprocal of 1/x, where x ≠ 0 is ________. (5) The product of two rational numbers is always a _______. (6) The reciprocal of a positive rational number is ________

We will use the definition of reciprocal to answer this question.

## Answer: (1) no (2) 1, -1 (3) 1/5 (4) x (5) rational number (6) positive rational number

The word reciprocal has its roots in Latin as the word “reciprocus” meaning “returning”. On taking reciprocal of an inverted number, it returns to the original number. The reciprocal of a given number when multiplied by that number gives one as a product. A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0. The set of rational numbers is denoted by Q.

**Explanation:**

(1) Zero has __no__ reciprocal.

(2) The numbers __1__ and __-1__ are their own reciprocals.

(3) The reciprocal of 5 is __1/5__.

(4) Reciprocal of 1/x, where x ≠ 0 is** **__x__.

(5) The product of two rational numbers is always a __rational number__.

(6) The reciprocal of a positive rational number is a __positive rational number__.