# Do you use mixed fractions?

I’m at the MATRIX conference in Leeds, where I’ve just been talking to Adam Atkinson. He told me that he’s trying to compile a definitive list of countries that don’t use mixed fractions.

Here’s a mixed fraction: $2 \frac{2}{3}$
And here’s a non-mixed fraction: $\frac{8}{3}$
Actually, here’s an interesting fact about that number: $2 \sqrt{ \frac{2}{3} } = \sqrt{ 2 \frac{2}{3} }$
This only makes sense if you believe in mixed fractions (and unicode character U+2062, “invisible times”)

This is going to be one of those wipe-your-bum-standing-up situations: it’s entirely possible that you can be on either side of this divide and not know the other exists. Apparently, in some countries mixed fractions just don’t exist: an integer written next to a fraction is incorrect.

So, to help Adam on his way, I thought I’d start another in our long-running series of Aperiodical Surveys. Please tell us where you live, and if mixed fractions are OK in your book.

• #### Christian Lawson-Perfect

Mathematician, koala fan, Aperiodical editor. Usually found paddling in the North Sea, or fiddling with computers.

### 4 Responses to “Do you use mixed fractions?”

1. Paul Taylor

Are we talking about just when ‘doing maths’? Or are there countries where you couldn’t even say “I’m on leave for the next 3½ days” or whatever?

For the record, some people in non-mixed-number countries might take “3 1/2” to be a product and say it was 1.5. To say “3 1/2 weeks” in Italian you would say “3 settimane e 1/2” so the query as posed doesn’t really constitute a problem. Don’t know about French, Spanish, Portuguese or Romanian. (Belgium and Switzerland also on the list, I was told at Matrix 2016). However, you can say the number “3 e 1/2” in Italian, so your question works if we remove the things there are 3 1/2 of. Maybe people would just write 3.5? This conversation tends to go along similar lines to the one involving learning there are places where “Mary”, “marry” and “merry” are homophones.

We saw some road signs near Leeds indicating towns e.g. 1 1/4 miles or 1 3/4 miles away.

There’s also a _temporal_ element to all of this. I am informed that Italy, Spain, Portugal and Switzerland used to have mixed numbers (within living memory) but no longer do. However, at least in the case of Italy we are talking about a good while ago. You might need to be 80+ now to have done them at school there. One of the Spanish contingent at Matrix said they vanished in Spain in the 60s.

I had imagined that South America might be full of countries without mixed numbers, but if it was colonized before mixed numbers were abolished in Spain and Portugal, then perhaps not.

At this point am also keen to know if France (and Belgium and Romania) _ever_ had mixed numbers. And if anywhere has switched from not having them to having them.

Note: I’ve had a few cases of people saying mixed numbers exist in (place) giving “3+1/2” as an example. I would not count it as a mixed number country if the + is obligatory. Also, some places apparently DO cover them at school as a usage found in foreign media or products, or as a thing that can be used in, say, shoe sizes but not for doing any kind of mathematical operation with. I’d count all of those as being places where mixed numbers did not exist.