It hapneth also some times, that the Quotient cannot be expressed by whole numbers, as 4 divided by 3 in this sort, whereby appeareth, that there will infinitly come from the 3 the rest of 1/3 and in such an accident you may come so neere as the thing requireth, omitting the remaynder…

— Simon Stevin, The Tenth (1585)^{1}

Many people find fractions and decimals confusing, counter-intuitive, and even scary. Consider the story of the A&W restaurant chain’s ill-fated third-of-a-pound burger, introduced as a beefier rival of the McDonald’s quarter-pounder. Many customers were unhappy that A&W was charging more for a third of a pound of beef than McDonald’s charged for a quarter of a pound. And why shouldn’t they be unhappy? Three is less than four, so one-third is less than one-fourth, right?

Well, that’s what many of those aggrieved customers told the consultants who had been hired to find out why A&W’s “Third is the Word!” innovation had gone so disastrously awry. But I wonder if those customers were rationalizing (sorry…) after the fact. Maybe some of these people had had such bad experiences when learning about fractions in school (the awkward fraction 1/3 in particular) that they preferred to avoid eating at establishments that triggered their math anxiety.

Perhaps part of the problem is that for many people, the standard middle school curriculum on fractions and decimals doesn’t hang together well, with its mélange of different representations of things that they’re told are really the same thing under different names, such as 1 1/5 and 6/5 and 12/10 and 1.2 (and let’s not even mention 120%). And as if that weren’t bad enough, there are decimals that never end?!? It’s easy to come away from this experience confused and disheartened.

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