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Funding for this project generously provided by Overdeck Family Foundation

around 1900–1600 BCE

Babylonian School Multiplication Tablet

Ancient multiplication exercises—with teacher and student errors

Reciprocal and multiplication tables were commonly composed in scribal schools of Sumer and Babylonia. They had relatively standard forms in which student scribes copied an original series of lines multiple times to reinforce "penmanship" as well as mastery and memorization of the facts. This exemplar originated in the ancient Sumerian city of Nippur around 1900–1600 BCE and was reassembled from fragments found by several separate archaeological expeditions.

Babylonian School Multiplication Tablet

The front of the tablet contains a teacher's (on the left) and student's (on the right) copy of the 45 times table. The reverse sides contains a list of divisors of 12,960,000 from 1 1/2 to 81 with quotients and a 50 times table written alternately three times. Both scribe's and student's copies contain a number of errors.

Artifact dimensions

17.3 in. × 11 in. × 3.3 in. (central portion, possibly omitting lower-right piece attached post-Hilprecht)

Original artifact location

Nippur (historical name), Afak, Al-Qadisiyah, Iraq (current name)

Current artifact location

Penn Museum, Philadelphia

Catalog number

CBS 11340 + CBS 11402 + UM 29-16-752


Counting timeline Sumerian Earliest Known Math Table Sumerian 7 Quotient and 10 Product Tablet Babylonian School Multiplication Tablet Babylonian Reciprocals Tablet Rhind Papyrus Roman Stylus Tablet Bamboo-Strip Multiplication Table Venerable Bede's De temporum ratione South American Quipu Aztec Dates from Codex Mendoza Midewiwin Birchbark Scroll

Interactive Content

Computational Explanation

Other Resources

Additional Reading

  • Hilprecht, H. V. Object 20 in Mathematical, Metrological and Chronological Tablets from the Temple Library of Nippur. Philadelphia, PA: Department of Archaeology, University of Pennsylvania, p. 60 and Pl. 10, 1906.
  • Neugebauer, O. Mathematische Keilschrift-Texte. Springer, pp. 12, 54 and 62, 1935.
  • Robson, E. Fig 1.4 in "Tables and tabular formatting in Sumer, Babylonia, and Assyria, 2500 BCE–50 CE." Ch. 1 in The History of Mathematical Tables: From Sumer to Spreadsheets (Ed. M Campbell-Kelly, M. Croarken, R. Flood and E. Robson). Oxford, England: Oxford University Press, p. 32, 2007. [misidentifies the tablet as CBS 2142]

Image Credits

Penn Museum