When a mixed quantity or a mixed number has to be multiplied by a large number, it is sometimes convenient to express the former in terms of one only of its denominations.
A fractional number is called a proper fraction or an improper fraction according as the numerator is or is not 3 less than the denominator; and an expression 4 such as 24 is called a mixed number.
An im 5 proper fraction is therefore equal either to an 2 I integer or to a mixed number.
It will be seen from § 17 that a mixed number corresponds with what is there called a mixed quantity.
They only apply accurately to divisions by 2, 4, 5, 10, 20, 25 or 50; but they have the convenience of fitting in with the denary scale of notation, and they can be extended to other divisions by using a mixed number as numerator.
