(i) The product of two positive rational numbers is always positive

(ii) The product of a positive rational number and a negative rational number is always negative

(iii) The product of two negative rational numbers is always positive

(iv) The reciprocal of a positive rational numbers is positive

(v) The reciprocal of a negative rational number is negative

(vi) The product of a rational number and its reciprocal is 1

(vii) Zero has no reciprocal

(viii) The numbers 1 and -1 are their own reciprocals

(ix) If a is reciprocal of b, then the reciprocal of b is a

(x) The number 0 is not the reciprocal of any number

(xi) Reciprocal of is a

(xii) (17 * 12)^-1 = 17^-1 * 12^-1