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Updated: May 5, 2025
No frontier picture is more familiar or more pleasing than that of the farmer's boy sitting or lying on the floor during the long winter evening industriously tracing by firelight or by candlelight the proverb or quotation assigned him as an exercise in penmanship, or wrestling with the intricacies of least common denominators and highest common divisors.
She quieted the trouble of her thoughts as well as she could before tea was over and the evening task of preparation, the gulfs and straits, the predicates and noun sentences, rule of three, common denominators, and all the dry-as-dust machinery was set in motion again.
In any plays whatever, you will find these apparitions and recollections. The dullest hero is given glorious visualizing power. These are some of the indestructible least common denominators of folk stories old and new. When skilfully used, they can all exercise a power over the audience, such as the crystal has over the crystal-gazer.
We have required him to solve problems containing fractions with large and irreducible denominators such as are never met in the business world, but he cannot readily and with certainty handle numbers expressed in halves, thirds, quarters, fifths, and eighths. He has been compelled to sacrifice practical business efficiency in number to an attempt to train his powers of logical analysis.
This official had asked the candidate, when he came for examination, to add together 2/3, 3/4, 5/6, and 7/8, whereupon he wrote: "Since you cannot reduce these fractions to a common denominator, I adopt the method of multiplying the numerators together for a new numerator, and the denominators together for a new denominator=210/576!
The numerator of the third is the sum of the numerators of the first and second, its denominator, the sum of the two denominators. The same is true of the fourth fraction and the two immediately preceding it. Continuing the series, we get the fractions 5/13, 8/21, 13/34.
In this respect education is like food: what is one man's meat is another man's poison. We do not wish to teach book-keeping to a washerwoman, or fancy ironing to a private secretary. Then, why stuff artisans, domestic servants, and farm labourers with common denominators and the rules of syntax?
Our conclusion is must be that you will not amuse, nor inform, nor help anybody; you will not amuse, nor better, nor inform yourselves; you will sink into a state in which you can neither show, nor feel, nor see, anything, but that one is to two as three is to six. And in that state what should we call ourselves? Men? I think not. The right name for us would be numerators and denominators.
This, reduced to the greatest common divisor, or, add numerators and denominators=17/21!"
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