Best Answer: let x be the number 9 times the reciprocal of a number is 9/x x Ã· 9/x = 1 x â¢ x/9 = 1 xÂ²/9 = 1 xÂ² = 9 x = 3 or -3. Source(s): gohpihan Â· gÃ´hpihÃ¡n 6 years. Ago thumbs. upeport Abuse. call the number n then 9 times its reciprocal = (9/n) The qotient of those two numbers is: n/(9/n) now set that equal to 1 and solve. n/(9/n)=1 multiply top and bottom by the LCD of n to get: n^2/9=1 now cross multiply and get: n^2=9 so n= +/-sqrt(9) Hope this helps. Susan Â· 6 years ago.