Interestingly enough, we do not have such a distinction in France. From the French Wikipedia article about fractions (emphasis mine):

Dans l'enseignement français depuis la fin du xixe siècle, la fraction est définie comme le quotient de deux nombres entiers sans contrainte sur la taille du numérateur et du dénominateur (...)

In French education, since the end of the 19th century, a fraction is defined as a division of two whole numbers, without constraints on the size of the numerator and denominator (...)

I think I recall that at the very, very first introduction of fractions my children saw the version $1\frac{3}{4}$ but it was quickly replaced by $\frac{7}{4}$ and never came back. I do not remember how it was when I was learning fractions, but I do not remember ever having used the $1\frac{3}{4}$ version.

On a related note, I find the $1\frac{3}{4}$ version particularly unintuitive, it suspiciously looks like $1\times \frac{3}{4}$.

Interestingly enough, we do not have such a distinction in France. From the French Wikipedia article about fractions (emphasis mine):

Dans l'enseignement français depuis la fin du xixe siècle, la fraction est définie comme le quotient de deux nombres entiers sans contrainte sur la taille du numérateur et du dénominateur (...)

In French education, since the end of the 19th century, a fraction is defined as a division of two whole numbers, without constraints on the size of the numerator and denominator (...)

I think I recall that at the very, very first introduction of fractions my children saw the version $1\frac{3}{4}$ but it was quickly replaced by $\frac{7}{4}$ and never came back. I do not remember how it was when I was learning fractions, but I do not remember ever having used the $1\frac{3}{4}$ version.

On a related note, I find the $1\frac{3}{4}$ version particularly unintuitive, it suspiciously looks like $1\times \frac{3}{4}$.

EDIT: Now that I think of it, it may be that the US use of proper vs improper fractions come from their very heavy use in measurements.

In Europe, we would never say that something is $1\frac{2}{11}$ meters. We would say it is 1,18 m (with a comma :)) - because of the decimal nature of the metric system.

We basically never have a need to use fractions in everyday life, only in calculations (where the "improper" form is easier to use)

Interestingly enough, we do not have such a distinction in France. From the French Wikipedia article about fractions (emphasis mine):

Dans l'enseignement français depuis la fin du xixe siècle, la fraction est définie comme le quotient de deux nombres entiers sans contrainte sur la taille du numérateur et du dénominateur (...)

In French education, since the end of the 19th century, a fraction is defined as a division of two whole numbers, without constraints on the size of the numerator and denominator (...)

I think I recall that at the very, very first introduction of fractions my children saw the version $1\frac{3}{4}$ but it was quickly replaced by $\frac{7}{4}$ and never came back.

On a related note, I find the $1\frac{3}{4}$ version particularly unintuitive, it suspiciously looks $1\times \frac{3}{4}$.

Interestingly enough, we do not have such a distinction in France. From the French Wikipedia article about fractions (emphasis mine):

Dans l'enseignement français depuis la fin du xixe siècle, la fraction est définie comme le quotient de deux nombres entiers sans contrainte sur la taille du numérateur et du dénominateur (...)

In French education, since the end of the 19th century, a fraction is defined as a division of two whole numbers, without constraints on the size of the numerator and denominator (...)

I think I recall that at the very, very first introduction of fractions my children saw the version $1\frac{3}{4}$ but it was quickly replaced by $\frac{7}{4}$ and never came back. I do not remember how it was when I was learning fractions, but I do not remember ever having used the $1\frac{3}{4}$ version.

On a related note, I find the $1\frac{3}{4}$ version particularly unintuitive, it suspiciously looks like $1\times \frac{3}{4}$.