Mixed numbers and people coming from non English speaking countries

[Arkadia]

Please, indulge me... :)

A few weeks ago I came a cross a notation like this
2 1/4
which I am told is a mixed number meaning (2+1/4), i.e. 9/4
After thinking about it, I have realized that this non standard notation must exist here because of the imperial system as even today you see written down "1 1/4 inches" and such like.

That is totally new to me. Normally (to me) (2 1/4) is ALWAYS the same as (2*1/4), i.e 2/4.

I must confess, I am surprised that in the UK (and the US, according to Khan Academy) such a notation is still used. In any case, I was wondering, where you are from (my not Englishasafirst_language friends) which way were you taught?

Also, going forward towards algebra, how is one supposed to know if in an expression comprising fractions and integers a + or a * sign is implied?

Maths is like a language.

The mixed number notation is a standard notation which once you are have learnt, have understood and are used to, means what it means.

Notation rules using numbers and letters are slightly different. In your 2 1/4 example, you have a X missing for it to mean 2/4.

But if they were letters instead of numbers, you would be correct.

But once learnt and understood. SHouldn't be a problem.

Well, this is the only occurrence I know of where a + sign is implied. It would cause confusion crossing borders, as it confused me when I saw it written down. This is why I was asking what people were taught.

Do you think 2¼ is also two times one quarter, or is it really just the lack of appropriate representation for the fraction in smaller typeface which is the problem?

The only time (as a over 40 year old native of England) that I've seen two and a quarter written as you did is when limited by typewriters, when doing it by hand or on modern systems the fraction is always written smaller, although obviously in mumsnet most wouldn't bother digging out the characters.

Sir, If I saw that I would read it with a * in the middle.
Thinking about it I have seen such notation here and there, but never really thought about it until, that is, the other day and I was found wanting ;)
In any caso, no, where I am from we would only use 2+1/4.
I wonder what the do in Eire, as they have gone completely metric and won't be using a great deal of fractions in every day life.

Intriguing. I've lived in 2 other non English countries and 2 1/4 has meant 2 and a quarter there. I don't think going metric means people stop using fractions. We are never really going to talk aboit .25 of an apple are we? Or .5 of a pizza?

2¼ means 'two and one-quarter'

2*¼ or 2×¼ would be 'two times one-quarter' and would be equal to ½.

That's the standard British mathematical notation.

In algebra we would normally use top-heavy fractions rather than mixed numbers to avoid confusion. You would see 3a/2 or 3/2 a not 1 1/2 a if you can see what I mean!

Eastern Europe,country with metric system and I spent many weeks reintegrating and simplifying the buggers(or whatever is called in english) .

I have lived in a couple of different Asian countries (not ex-British colonies), and 2¼ there meant exactly what it does here - two and a quarter. I'm really curious to know where it is that this means two times a quarter, as I have never come across this anywhere!

my, if I were to write "one and a half", I would write 1.5, but speak it "one and a half" when talking about pizzas or litres of milk.
The other day (I do live a sad life...) I even checked a primary school book and seen that mixed number always have a + in the middle, which is what I remember from my school days.

I'd love to know where that's from. I've never seen it written with a plus sign unless it's a sum.

my, but it is a sum ;)

Check here for example:
www.youmath.it/scuola-primaria/matematica-scuola-primaria/quarta-elementare/2117-numero-misto.html

Is it Italy, then? Interesting. I wonder if the systematicity of it is related in any way to the (near) 1-1 correspondence between letters and sounds that you find in Italian, too?
In my non-English speaking, completely metric part of the world, 2 1/4 would be interpreted as 2+1/4 and it never even occurred to me to see anything strange about it, until I heard the English expression 'mixed numbers' and started thinking about what that may be. In Algebra, of course, any relation between 'numbers' would be made explicit so you would never see e.g. '2 3' and assume it meant two threes, but when mixing letters with numbers then putting them next to each other would assume multiplication: 2a would mean two a's, unambiguously, rather than 2 and a. It can be 2+3 or 2x3 but never 2 3. It can be 2+1/4 or 2x1/4 but never just 2 1/4 (in algebra; though it is, obviously, in 'daily life'). Unlike when mixing numbers and 'letters' where it can be 2+a or 2a, where, in the latter, the multiplication is not made explicit by using a symbol.

I can see DS having more trouble with that though! Seeing as he learned Algebra through playing Dragonbox, and thus learned about numbers/symbols next to each other (touching) being linked (according to the rules of multiplication, though you do not need to understand multiplication in order to understand the rules according to which they are linked). I can see him intuitively reading 2 1/4 as 2 times 1/4 rather than 2 and 1/4. Hmmm.

It's funny, though, that you can put a number next to a letter and it is clear that it implies a multiplication, but you cannot do the same with two numbers. Perhaps it is because of the physical nearness? If you put two numbers close together, it makes a new number because one number's place value changes.
Which explains why you CAN put 2(3+4) and everyone knows that it is 14, not 9. But you cannot put 2 7 and assume multiplication, because you can't get the 2 and 7 close enough to each other without turning them into 27...?
Whereas if you want to express twenty something, with the something being unknown, you cannot put 2x because everyone would read that as 2 times x. You'd have to go 'complicated' and put (20 + x) with x being constrained to natural numbers

I'm a mathematician and I have never (despite doing maths with various nationalities) come across 2 1/4 meaning 2x 1/4.
If I was implying that, then I'd put a "." in the middle, so 2.1/4 as it's fairly universal to mean 9/4.

I grew up in Australia lesrningonly the metric system. That was pretty standard. My parents from USSR and also consider that self explanatory.

I grew up in two different countries( USA and my native non English speaking country), and mixed numbers like 2 1/4 always existed even decades ago when I was in school. It never meant 2 x 1/4, it always meant 2 + 1/4.

I am German and 2 1/4 means for me 2 and one quarter. 2.25 may also be correct but when we did fractions in school (35+ years ago) we obviously had to write it as 2 1/4.

DD is in Y6 here in England and writes it this way.

It really intrigued me, which country teach 2 1/4 as 2 x 1/4?
Can you elaborate?