An improper fraction is one whose denominator is less than its numerator. Taking this explanation into account, we can say that 4/3, to name a case, is an improper fraction. Its numerator is 4 and its denominator is 3: As you can see, the numerator is greater than the denominator. If we solve the division, we will notice that the result is greater than 1: 1.33.
A fraction is an expression that refers to a division. It is made up of two numbers separated by a dividing line: the numerator (found on this line) is the number that is divided, while the denominator (that appears below the line) is the amount by which it is divided. When the numerator and denominator are equal, we know that it is then a whole number written as a fraction, for example 6/6. It is commonly said that this type of fraction is improper.
If what we want is to pass an improper fraction to a mixed number, what we must do is divide the numerator by the denominator. The quotient will be the integer that belongs to the mixed number and the remainder will be the numerator of the fraction, while the denominator will remain the same.
We must be clear that it is always possible, in case of having an improper fraction, to decompose it into the sum of a whole number plus a proper fraction in which the numerator is smaller than the denominator.
For mathematics, improper fractions are currently easier to use than mixed fractions. But, for everyday use, people understand mixed numbers better.
The exercise of transforming an improper fraction into a mixed number is simple: we must decompose the numerator in such a way that it is divisible by the denominator, resulting in a whole number (in the example, 4/2 = 2), the remaining fraction (in this case ½) will be the fraction.
For the purposes of mathematical analysis, it is useless to express an improper fraction as the number of units it has and the quotient of less than one, since what matters is each number separately: operations between fractions, as well as those that combine fractions and whole numbers, they are much simpler as you work with improper fractions.
Although the operations between proper and improper fractions are performed in the same way, there are certain differential characteristics in both cases, such as the fact that a multiplication between improper fractions results in a proper fraction.