**Fraction** comes from the Latin word *frangere*, to break. A fraction, then, originally represented the broken portion of some whole. The first known use of the word in English is by Geoffrey Chaucer in 1391 in the work, A Treatise on the Astrolabe. Although mostly remembered today for The Canterbury Tales, he was far more famous in his lifetime for this scientific work. The treatise is considered the oldest work in English written on a complex scientific Instrument.

By the middle of the 19th Century fraction was used to describe parts larger than the whole as well. In the 1876 edition of __Davies' Practical Arithmetic__ he lists as Article 114. "There are six kinds of fractions:" He then goes on to define

"1.A Proper Fractionis one whose numerator is less than the denominator" Proper fractions are often called "vulgar factions", or common fractions as the term vulgar in Latin referred to "characteristic of or belonging to the masses."

2.An Improper Fractionis one whose numerator is equal to, or exceeds the denominator."

"3.A Simple Fractionis one whose numerator and denominator are both whole numbers." (Note this is not necessarily what modern teachers would call in "simplest form", for example 8/4 is a simple fraction)

"4.A Compound Fractionis a fraction of a fraction or several fractions connected by the wordofor x. The following are compound fractions: 1/2 of 1/4, 1/3 of 1/3 of 1/3, 1/7 x 1/3 x 4."

"5.A Mixed Numberis a number expressed by an integer and a fraction."

"6. AComplex Fractionis one whose numerator or denominator is fractional; or, in which both are fractional," In the Fourth Yearbook of the NCTM in 1929 one of the curriculum changes listed for the State of New York included in the list for the 1910 syllabus, "Fractions, including complex fractions of the'apartment house'type." (page 161) I assume the "mixed number over a mixed number" is the type of problem referred to, but am still trying to find confirmation of this.

In the Late 1930's and 40's arithmetic textbooks seemed to have totally omitted the broader definition, and treat reduce as a *vade mecam* for fractions in "lowest terms" or "simplest terms". In __Learning Arithmetic __ by Lennes, Rogers and Traver, (1942) the term reduction appears in the index only as a subheading under "fractions". The first occurrence in the text, on page 36, without prior definition introduces students to a set of problems with the directions, "Reduce the fractions below to simplest forms". In __Making Sure of Arithmetic__ by Silver Burdett (1955) the word "reduce" does not appear in the index at all, but on page 8 it contains, "When the two terms of a fraction are divided by the same number until there is no number by which both terms can be divided evenly, the fraction is reduced to **lowest terms**." [emphasis is from text]. By 1964, __The Universal Encyclopedia of Mathematics__ by Simon and Schuster contains "A fraction is reduced, or cancelled, by dividing numerator and denominator by the same number." (pg 364) Later on the same page they note, "a fraction cannot be reduced if numerator and denominator are mutually prime" indicating that when they said "the same number" in the first statement, they meant a positive integer. This definition leads to "reduction" of fractions as making the numerator and denominator both smaller.

The roots of the word reduce are from the Latin *re* for back or again, and *dicere* which means "to lead". The latter root is also found in the word *educare* which is literally, to lead out, and is the source of our modern English word, educate.

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