Mixed numbers can be a source of great confusion for some students because the mathematical convention is usually that when two things are juxtaposed they are being multiplied. However, in a mixed fraction the two components are being added. This is simply a matter of convention, but that's of little comfort to many students who are confused, but don't know it until things all go horribly wrong. Major can of worms. In general in the English speaking world, mixed numbers are used in "real life" so it's relevant that they should be taught. However in some countries the expression $3\frac{1}{2}$ is neither understood nor used.
When we have a quantity that is partway between two counting numbers (or integers) then we usually say something like "three and a half." This is referred to as a "Mixed number" because it consists of a whole number and a fraction, mixed together.

A Mixed Number can be converted to a rational number, so:

• $3\frac{1}{2}~=~\frac{7}{2}$
For a (positive) mixed number greater than 1, the resulting fraction is an improper fraction.

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