4 December 2023

According to its general concept in mathematics, fractions are quantities expressed as a division between others. These are classified into 3 types: own, whose value is less than the denominator; improper, whose numerator is greater than or equal to the denominator; and mixed, composed of a whole number and a proper fraction.

## Definition and concept of an improper fraction

The fraction is characterized by its denominator is less than its numerator, that is, the lower figure is greater than the upper one. In mathematics, its importance lies in the fact that it can be converted into mixed quantities or into decimals. Furthermore, they are used in solving proportion problems and in performing arithmetic operations such as addition, subtraction, multiplication, and division of fractions.

Likewise, they are Fundamentals in Simplifying Algebraic Operations and in solving fractional equations. Knowledge of it is key in the study and solution of arithmetic problems, from the basic to the advanced level.

In algebra, they are used to represent the irrational numbers or quantities They cannot be expressed in whole numbers. In the same way, they are used to simplify complex algebraic expressions.

To identify a fraction, any whole number that is written as a portion where the denominator is 1 can be taken as a reference. There is the unit of measure that symbolizes the identical fraction and that represents equal quantities for the numerator and denominator. This arithmetic value is important to understand the concept of fractions.

Therefore, when a whole quantity is found in a fraction, can be written as a decimal or as a fraction with a denominator of 1, and then add or subtract it as needed. It is important to use the appropriate punctuation marks to give fluidity and coherence to the text.

## What are the properties of an improper fraction?

Some of its peculiarities are:

• can be convert to mixed fractions if the numerator is divided by the denominator and the result is reflected as a whole number and the remainder as a fraction.
• When compared to other fractions, they can be find common divisors and compare the number of parts.
• By adding or subtracting them, the result can be a distinct improper fractiona mixed number, or an integer.
• If multiplied by an integer, the result will be another improper fraction.
• If they are divided by an integer, the result can be another improper fraction or a mixed number.

In this process, the implementation of the addition of fractions with different denominators is also considered. For this development, the first thing to do is find a common divisor that be the least common multiple among the existing denominators. Then, each part is multiplied by the number that has multiplied the divisor, and at the end the results obtained are added and the same denominator is left.

The least common multiple is a concept that is used continuously in mathematics and can be implemented in the sum of fractions with unlike denominators. Taking this value into account for the denominators, Fractions can be converted to equivalents and then add them. Regarding division, it is directly related to improper fractions, since it allows us to simplify the procedure and obtain a proper fraction that represents the result of the operation.

## Difference between an improper fraction and a mixed one

The main difference between them is that the improper ones are represented by a larger quantity, while the mixed ones are made up of integers and a fraction. A mixed fraction is an expression combining a whole number and a fractionand to make it improper, multiply the denominator by the whole number and add the result to the numerator of the fraction.

Conversely, to convert an improper fraction to a mixed one, divide the numerator by the denominator and represent the quotient as a whole number and a proper fraction. It is important to keep in mind that a mixed number is a mathematical form to symbolize a part that is greater than unity, or what is the same, to represent fractions in which the denominator is less than the numerator.

## How do improper fractions originate?

Improper fractions are generated when the numerator is greater than or equal to the denominator. can also be get by adding or subtracting fractions with unlike denominators which result in a larger numerator. It is always important to consider that they can be transformed into mixed quantities, where the whole is the complete part of the portion and the remainder is the fractional part.

## Examples of an improper fraction in mathematics

Next I present examples of improper fractions which can be used in different areas, sciences and studies in a variety of contexts, such as economics, for example, where it is used to calculate the unit value of production:

• 7/4: In this case, the numerator (7) is greater than the denominator (4), making it an improper fraction.

• 3/10: Again, the numerator (10) is greater than the denominator (3), making this fraction an improper fraction.

• 5/2: Here, the numerator (5) is greater than the denominator (2), making it an improper fraction.

• 11/6: The numerator (11) is greater than the denominator (6), which makes this fraction improper.

• 8/17: In this case, the numerator (17) is greater than the denominator (8), making this fraction an improper fraction.

Knowing the cost per unit of a good or service is important to setting the selling price, covering all costs, and making a clear profit. To do this, divide the total amount of expenses divided by the volume produced, which results in an improper fraction that represents the unit cost.

In making investment decisions, the rate of return can be calculated by dividing the net profit by the total investment. If the result is an improper fraction, indicates that the transaction is not profitable and more resources are needed to obtain the expected profits.

Likewise, in the default analysis, it is essential to evaluate the ability to pay when a person or company has debts to settle. To do it, it can calculate the relationship between debt and revenue or total assets. If the result is an improper fraction, it indicates that the ability to pay is not feasible and measures are needed to reduce debt or increase income.