Fractions in Old Algebra Book

16-year-old Helena Muffly wrote exactly 100 years ago today: 

Thursday, November 23, 1911: Am working at my algebra in the evening so I can make a better mark than I did last month. If it isn’t any better I will be beyond all hope.

 Her middle-aged granddaughter’s comments 100 years later:

In October Grandma struggled mightily with algebra—the topic was least common multiples (L.C.M.) and highest common factors (H.C.F.)—and she ended up getting a 68% on the exam.

I’m not sure what Grandma was working on in November—but in one early 20th century algebra book—Durrell’s School Algebra, the chapter after L.C.M. and H.C.F. was Fractions.

The book says:

In algebra, a fraction is often useful in expressing a general formula

Here are a couple of exercises from the book:

1. If three boys weigh a, b, c pounds respectively, what is their average weight?

2. If sugar is worth a cents a pound, how many pounds can be obtained in exchange for b pounds of butter worth c cents a pound?

3. If coal is worth c dollars a ton, how many tons can be obtained in exchange for f bushels of wheat worth h cents a bushel and for w bushels of corn worth y cents a bushel?

4 Responses

  1. Too many unknowns!!

  2. The answer? Alphabet soup!

    Happy Thanksgiving!

  3. Yes, it’s an alphabet soup!

    I don’t have an answer key, but I think that the answers are:
    1. (a + b + c)/3
    2. ab/c
    3. fc/h + wc/y

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