# Who introduced the mixed fraction notation?

Who introduced mixed fraction notation? This notion is a source of confusion to me because it may be interpreted as multiplication.

• Please don't write in ALL-CAPS.
– Danu
Nov 11, 2022 at 14:01
• I would guess notation $2\frac12$ is far, far older than juxtaposition for multiplication. And older than decimals $2.5$ for fractions. Nov 12, 2022 at 12:11

in 1202, Leonardo of Pisa (= Fibonacci) was the first European to do it, but Arabic writers preceded him. He wrote the fraction to the left of the whole number (e.g. $$\frac12 12$$) following the Arabic usage; note that Arabic is written right-to-left. At the time it was not confusing, because he did not write products by juxtaposition.

In Wikipedia we find a discussion of historical notations for fractions. In particular

The same fractional notation—with the fraction given before the integer[30]—appears soon after in the work of Leonardo Fibonacci in the 13th century.[33]

References are
[30] Miller, Jeff (22 December 2014). "Earliest Uses of Various Mathematical Symbols" link

The horizontal fraction bar was introduced by the Arabs. "The Arabs at first copied the Hindu notation, but later improved on it by inserting a horizontal bar between the two numbers" (Burton).
Several sources attribute the horizontal fraction bar to al-Hassar around 1200.
When Rabbi ben Ezra (c. 1140) adopted the Moorish forms he generally omitted the bar.
Fibonacci (c.1175-1250) was the first European mathematician to use the fraction bar as it is used today. He followed the Arab practice of placing the fraction to the left of the integer (Cajori vol. 1, page 311).
According to the DSB, Abu Abdallah Yaish ibn Ibrahim ibn Yusuf ibn Simak al-Umawi (14th or 15th century) insisted that the horizontal fraction bar be used, whereas easterners continued to write it without the bar.
The bar is generally found in Latin manuscripts of the late Middle Ages, but when printing was introduced it was frequently omitted, doubtless owing to typographical difficulties. This inference is confirmed by such books as Rudolff's Kunstliche rechnung (1526), where the bar is omitted in all ordinary fractions but is inserted in fractions printed in larger type and those having large numbers (Smith vol. 2, page 216).

[33] Cajori (1928), p. 89 link