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MATH FUN CAN appear in the oddest places: in quick-food marketing or in mattress sales, to name two.

McDonald’s was ahead of its time in 1972 with supersizing a hamburger into the Quarter Pounder, which caught on big time and continues to this day. Sure, the Golden Arches’ standard burger is still available, but the Quarter Pounder has meat weighing a full one-quarter of a pound, at least early in its preparation.

The A&W chain would be justified in thinking McDonald’s (founded in 1940, reorganized as a burger stand in 1948) as a Ronald-Come-Lately. A&W began selling its root beer in 1919 and opened its first restaurants in 1922.

Iin the early 1980s, this older, albeit smaller chain decided to enter a war of fractions with McDonald’s by introducing the A&W Third Pounder. Not only did it contain one-twelfth-pound more meat, the Third Pounder had all the other necessary fixings—and cost no more than McDonald’s Quarter Pounder.

What’s more, people taking part in blind testing said the A&W Third Pounder tasted better than McDonald’s Quarter Pounder.

Despite this, the A&W Third Pounder failed in the marketplace, because many of its customers felt cheated.

A&W’s Alfred Taubman summed it up by reporting focus group results: “More than half of the participants in the Yankelovich focus groups questioned the price of our burger. ‘Why,’ they asked, ‘should we pay the same amount for a third of a pound of meat as we do for a quarter-pound of meat at McDonald’s? You’re overcharging us.’ Honestly. People thought a third of a pound was less than a quarter of a pound. After all, three is less than four!”

In 2007, even McDonald’s tested America’s mathematical acuity with the Angus Third Pounder. In 2015 it tried the Sirloin Third Pounder. These perceived lightweights are gone too.

Fellow math teachers of America, where have we screwed up?

Wouldn’t this graphic stick in the mind of any elementary school kid? Or are fractions more subtle than this?

I checked matters out with *Merriam-Webster,* which notes that “a fraction is a numerical representation indicating the quotient of two numbers.” That is, a/b.

Easy-peasy, however I admit there are some interesting implications here beyond burger sizes. In particular, there’s nothing that says the number on top (the numerator) has to be smaller than the number on the bottom (the denominator): For instance, 6/5 is a perfectly good fraction, a legitimate number equivalent to 1 1/5 or 1.2, and thus bigger than 1.

I conclude by examining the fallacy of an oft-heard advertising pitch: “Buy this mattress at *a fraction* of its usual price! Today, it’s only $600!”

In truth, its usual price may be $500. But, sure enough, 600/500 is a legitimate fraction (equal to 6/5, of course, by the Gozinta Rule: “100 goes into 600 six times; it goes into 500 five times”).

So the mattress company’s lawyers are happy with the wording. On the other hand, that “on sale” mattress actually costs 1/5 or 0.2 or 20 percent more. Some deal, eh?

Is this flabby English or flabby math? Or a little of both? You’ll note that my hands never leave my wrists. ds

© Dennis Simanaitis, SimanaitisSays.com, 2016

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Percentages seem to be a problem for many as well– i.e., until it is pointed out that each cent in a dollar represents one percent of the (100%) dollar.

Why is it so difficult for many to understand that 120% is the same as your 6/5ths example? But tell them that 120%=120 pennies, and they know the answer.

A good analogy, Dwight.

(Although I also recall a person who was convinced there were 25 minutes in a quarter of a hour….)