The full text of the Teaching on Numbers by Kirik the Novgorodian is found in two 16th century manuscripts. One of them, which until the 1980s was known only in a 19th century copy, lacks a fragment about so called fractional hours that is present in the other manuscript. This circumstance gave rise to doubts concerning the authenticity of this fragment. In the 1980s, E. K. Piotrovskaia rediscovered this manuscript and showed that the place where the fragment about “fractional hours” was supposed to be was cut out of the sheet, thus, most likely, it was originally there. Thus, the content of the two main recensions was identical and therefore very weighty arguments would be required in order to question any part of the text. However, uncertainty about the authenticity of this part of the text for some reason is still found in studies devoted to the Teaching on Numbers. This is prompted both by the composition of the text (V. V. Mil’kov and R. A. Simonov) and by its grammar (V. V. Ivanov). The present paper discusses all the arguments against the authenticity of the “fractional hour” fragment and concludes that it belongs to the original text.