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Vulgar Fractions

Asya Simons

Asya Simons, digitization intern, Summer 2011

The following blog was written by Asya Simons who just completed her summer internship with the web and digital resources department at the VHS.  This is the last in a series of entries that she has written about her internship and specifically on her experience working on Unknown No Longer: A Database of Virginia Slave Names, which launches on September 15, 2011.


~Meg M. Eastman, digital collections manager

Periodically the Virginia Historical Society will post content created by guest writers. The opinions expressed are theirs alone and do not necessarily reflect the opinions of the Virginia Historical Society, its members, or its staff. The Virginia Historical Society encourages discussion; however, we reserve the right to remove posts that are offensive, threatening, or insulting.

I’ve never liked math. It can easily be called my worst subject; one I avoided at all costs until my high school graduation. Even when it came to college, I think I subconsciously chose a school with lax math requirements. That’s why I was amazed when I became fascinated with an arithmetic book in the collections of the Virginia Historical Society.

I first came across the book as a document that needed to be photographed for Unknown No Longer, the society’s slave name database. On the very last page was a deed containing a slave’s name, and for the project, that’s all I was interested in. I couldn’t help flipping through the book, however, as I passed the time in between photographs, and I realized I had never thought about math books existing in any form other than traditional textbooks. Sure, the book contained multiplication and division, and each section began with instructions, but it seemed to be geared toward farmers to assist with their business transactions.


Addition of Apothocary Weight, Cloth Measure, Dry Measure and Liquid Measure (Virginia Historical Society, Mss5:4 H3835:1, pages 4-5)

One of the first pages offers ways to add apothecary weights, cloth lengths, dry measurements and liquid measurements, followed by respective subtraction methods. The reader is given an opportunity to practice their new skills with word problems. The last word problem before learning multiplication employs history as well as arithmetic; it asks, “Gen. Washington died in 1799 how long has he been dead.” I wish my textbooks were that straightforward!

Word Problem

Word problem (Virginia Historical Society, Mss5:4 H3835:1, page 12)

The book then goes on to teach multiplication, division, simple and compounded interest, geometry, and “vulgar fractions.” Since I had never heard a math teacher refer to fractions as “vulgar” before, I was interested to find out what that term meant. I was slightly disappointed to find out that they were no more than fractions expressed as ¾, rather than in decimal form.

Vulgar Fractions

Vulgar Fractions (Virginia Historical Society, Mss5:4 H3835:1, page 142)

As the summer comes to a close and I prepare to head back to school, I know I still won’t be voluntarily taking a math course, and I’ll still cringe a little bit when I come across “vulgar” fractions from day to day. However, from now on, every arithmetic book I see will remind me that years ago those numbers represented a person’s livelihood. I am reminded that, even today, there has to be a practical application for all those formulas somewhere out there. Maybe math isn’t completely pointless after all.

The arithmetic book discussed here was kept by John Henderson (b. 1802) in Spotsylvania County, Va from 1817-1824 (Virginia Historical Society, Mss5:4 H3835:1).

One Comment leave one →
  1. Warren Jones permalink
    10/09/2013 10:56 am

    I am curious about how they taught how to add and subtract fractions. I was raised with the “find the common denominator” method, and I knew of no other method until it was much too late. There is a vastly superior method, and I’m curious as to the methods used in the past.


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