Considering fractions as proportional relationships between two numbers, a differentiation is established between those that exceed unity, called **improper fractions**, and those that do not, which are their own. For example: *4/3, 21/11, 50/18*.

## Characteristics of improper fractions

In improper fractions, the numerator (the number that is above in the fraction) is always greater than its denominator (the one that is below), so it can also be expressed as the combination of an integer and a fractional number and less than 1 .

We speak of ‘combination’, because in writing they appear that way: the whole number and to the right of it the fractional number. Although formally a ‘+’ sign should be written between the two, this is usually not done.

Those numbers made up of an integer and a fraction are called mixed numbers, and they are often seen on signs in shops that sell products by weight.

For example, in an ice cream parlor, it is difficult for someone to choose to order 5/2 of a kilo of ice cream (and much less in a higher ratio, such as 25/10), but they will surely request 2 ½, that is, “two and a half kilos” of ice cream.

The exercise of transforming an improper fraction into a mixed number is simple: you have to decompose the numerator in such a way that it is divisible by the denominator, resulting in an integer (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 smaller quotient of one, since what matters is each number separately: the operations between fractions, as well as those that combine fractions and whole numbers, are much simpler to the extent that one works with improper fractions.

Although the operations between proper and improper fractions are carried out in the same way, there are certain differential characteristics in both cases, such as the fact that a multiplication between improper fractions results in an improper fraction.

*(Improper Fractions)*

While the division between improper fractions depends precisely on which number is located as dividend (numerator) and which as divisor (denominator): if the first is greater than the second, then it will be an improper fraction, while if the second is the largest will be a proper fraction.

A particular case of improper fractions are those that result in a division in which there is no remainder, that is, one in which the numerator is a multiple of the denominator and therefore it is an integer: these are known as apparent fractions .

## Examples of Improper Fractions

Here are a few examples of improper fractions:

- 4/3
- 11/21
- 50/18
- 100/17
- 9/10
- 8/23
- 33/4
- 9/21
- 72/33
- 8/41
- 11/10
- 3/2
- 7/17
- 6/5
- 41/5
- 100/99
- 414/200
- 121/100
- 77/10
- 9/32

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