Weird number

I’ve got a loaner car while the TSX (my daughter’s graduation present) is tuned up. It’s free as long as I bring it back with the same amount of gas.

“It’s got 3/8 of a tank now,” said the 30ish guy. “That’s less than half a tank but more than . . . ”

“I know what 3/8 is,” I said.

“Well, people complain I use these weird numbers,” he said. “They want to know if it’s more than 1/4.”

“I went to school in the old days,” I said. “We learned what 3/8 is. It’s not a weird number.”

1. Cris says:

For real fun, try telling the guy at the deli counter that you want 3/8 of a pound of roast beef, and see how much you actually get.

2. Sad, sad, sad. Though my car’s fuel guage doesn’t have markings at the eighths, so I’d have to eyeball halfway between the 1/4 and the 1/2 markings.

3. If you really wanted to mess with him, you might ask “What percent is that?”

4. momof4 says:

Two years ago, my college-age son and I tried to order 2/3 pound of deli turkey and 1/3 pound of ham in a supermaket deli in a large Western town. The teenaged clerk told us that couldn’t be done, despite a digital scale sitting on the counter. Asked to keep adding turkey until the scale reached 0.67, she called for her supervisor. It was obvious the supervisor didn’t understand the relationship between 2/3 and .67 either, but she did as asked.

5. Hmm. I tend to take it easy on the grocery store folks. At least in our area, the local chains all hire a large number of people with cognitive disabilities — and pay them a union wage that allows them to pay some rent. I am often helped (well) by former students whom I know have IQ’s in the sub-normal range.

I stopped in at a nursery today, told the young man what area I needed sod for, and he calculated it in his head and put the right number of sections in my truck.

6. Thank you, Lightly Seasoned, for some perspective and a good counter example. We might wonder if a few anecdotes mean all that much. Unfortunately the bad examples seem to predominate, so I am of the opinion that the general level of mathematical knowledge, and I’m talking of arithmetic here, elementary school stuff, is substantially below what it could and should be in our society.

And, unfortunately, I’ve got more. As a math college teacher I see lots of evidence that many of my students can’t handle fractions. So, if I may, I will once again plug my article, Fractions My Algebra Students Can’t Do.

And, I think the general public is pretty weak in elementary science too. Here’s, some evidence of that, (as if copper bracelets, magnets, and horoscopes were not enough).

7. “…hydrogen is no more a source of energy than a wallet is a source of money!” —Brian Rude

I don’t know if that’s a “Rude Original” but I like it either way.

8. Brian…Wowzers.

Honestly, my 11 yr. old daughter could do the quiz in your article. Thank goodness for Singapore Math and Key to Fractions.

9. Richard Nieporent says:

I thought for a moment that you were going to tell us that the number on the license plate was 1729.

10. Devilbunny says:

Brian, your article is rather longer than I have the patience to read right now… but when you say

One type of problem in particular interests me, exemplified by 6 ¾ – 2 3/8 (corresponding to number 9 above, addition or subtraction of mixed numbers with or without borrowing and unlike denominators). I expect them to convert ¾ to 6/8 and then subtract the 3/8. Almost invariably that is not the way they do it. They change 6 ¾ to 27/4, change the 2 3/8 to 19/8, and then, (at least the ones who can actually do the problem) get a common denominator and proceed. I ask them if that is the way they were taught. Usually they say they can’t remember, it was a long time ago. Then I show them that they can leave the whole numbers alone, just change ¾ to 6/8, subtract the 3/8, and then deal with the whole numbers. They seem to make sense of this, but don’t necessarily think of it as a better way.

there’s a reason your students do it the way they do: it works no matter whether you have to carry or not. It’s not always the fastest way, but can you expect them to know at the outset whether 19/48 is more or less than 11/31? I do it the way your better students do, in most cases, because getting a BS in chemistry taught me that trying to do things in your head using shortcuts often leads to error; but meticulously spelling out every step, though a giant pain, produces correct answers.

11. Redkudu says:

>>”Hmm. I tend to take it easy on the grocery store folks. At least in our area, the local chains all hire a large number of people with cognitive disabilities — and pay them a union wage that allows them to pay some rent.”

>>”Thank you, Lightly Seasoned, for some perspective and a good counter example.”

Agreed. Same thing happens in my area.

12. PolishPlankton says:

Richard,

That would have been amazing! The lowest number that is the sum of two cubes, two different ways!

Ramanujan would have been impressed anyway.

13. It wouldn’t be the fraction thing that bothered me, it’s the non-full tank. I hate that. I always end up putting in more gas than I need to because you can’t tell while you’re pumping, where the little needle is.

So, I’d be bugged by the request. Just have everyone put the tank back to full.

14. momof4 says:

Neither my son nor I felt that the teenaged clerk was operating under a cognitive disability, although we might have been mistaken, but the department head certainly was not. Neither of them had learned the relationship between fractions and decimals. My two younger kids were exposed to it in school, although not expected to actually learn it, as their older siblings had done. That was done at home, along with the percentages.

15. Sister Howitzer says:

This reminds me of the Turkey problem.

16. Bart says:

> I wondered just how the nitrogen is obtained.

They probably recover it from old tires from which the oxygen has already leaked out.

17. Bart says:

Sorry, “…out from which the oxygen has already leaked.”

18. Your anecdote reminded me of when someone asked me how old my toddler was and I told her that he was 18 months old. Her reply:

“18 months? How old is that really? Why do you parents always use months? Nobody knows how many years that is!”

19. Tom in GA says:

I don’t care if everyone can do algebra. It’s perfectly fine in my opinion if a majority of society doesn’t know how to solve a quadratic equation, simplify a complex fraction, or graph a rational function.

I’m stunned at the willingness to accept stupidity when it comes to arithmetic however. Understanding and being able to manipulate fractions, decimals, and percentages should be a starting point for every adult in society. Numeracy is just as important as literacy.

20. Richard Nieporent says:

Right, PolishPlankton. I’m glad someone got the reference!

During an illness in England, Hardy visited Ramanujan in the hospital. When Hardy remarked that he had taken taxi number 1729, a singularly unexceptional number, Ramanujan immediately responded that this number was actually quite remarkable: it is the smallest integer that can be represented in two ways by the sum of two cubes: 1729=1^3+12^3=9^3+10^3.

By the way, Futurama contains several references to the Hardy–Ramanujan number.

http://theinfosphere.org/1729