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1543 R. Record Ground of Artes i. sig. M.iii^v Reduction is, by which all summes of grosse denomination, may be turned into summes of more subtyle denomination: and contrary wayes.

1649 F. Holyoake Riders Dict. (new ed.) sig. Dd1b In the reduction of these auncient measures to this equality with our English assise, I have had respect only to Troy weight.

1678 J. Hawkins Cocker's Arithm. viii. 104 Reduction Descending, is when it is Required to Reduce a Sum or Number of a greater Denomination, into a lesser... Reduction Ascending, is when it is Required to Reduce or bring a Sum or Number of a smaller Denomination into a Greater.

1774 W. Perry Man of Business 75 Reduction Descending and Ascending is performed by both Multiplication and Division... Examples. 1. In 84 l. how many pence and half crowns? Answer, 20160 pence, 672 half crowns.

1870 in P. Horn Village Educ. in 19th-cent. Oxfordshire (1979) 27 [Nov. 22] Taught reduction to Standards IV, V.

1925 Elem. School Jrnl. 25 672 [‘Arithmetic One Hundred Years Ago’] A large part of the pupils' time was taken up with mastering these reductions. They were subdivided into reduction ascending and reduction descending. It was pointed out to the pupil that the former term was objectionable because we do not ‘reduce’ when small units are expressed in terms of larger units, as when shillings are expressed in pounds.