2 March 2024

Mathematics is an incredibly broad field that encompasses a wide range of concepts and topics, each with its own unique set of principles and characteristics. Among the many ideas within mathematics is the concept of fractionswhich is a crucial element in everyday arithmetic.

However, not all fractions are equal: Some are classified as proper fractions and others are complex fractions. Proper fractions are an essential component in elementary mathematics and continue to be relevant in more advanced fields. So what exactly is a proper fraction?

A proper fraction is a fraction where the numerator, or the number above, is smaller than the denominator, or the number below. In other words, the value of the fraction is always less than one. Proper fractions are integrals to represent a part or a portion of something, like a slice of pizza or a fraction of a budget.

Furthermore, they play an important role in many mathematical operations such as addition, subtraction, multiplication, and division.

## Concept and definition of proper fractions

In mathematics, a proper fraction is a fraction in which the numerator (the top number) is smaller than the denominator (the number below). Simply put, proper fractions are those that represent a value less than one.

For example, 2/5 is a proper fraction because the numerator 2 is smaller than the denominator 5 and represents the value 0.4. By contrast, an improper fraction has a numerator that is equal to or greater than the denominator and represents a value greater than one.

For example, 7/5 is an improper fraction because the numerator 7 is greater than the denominator 5 and represents the value 1.4. In general, the concept of proper fractions is fundamental to studying fractions and understanding their characteristics in mathematics.

It is crucial to differentiate proper fractions from other types of fractions when performing operations such as addition, subtraction, multiplication, and division. Proper fractions have specific properties that clearly distinguish them from improper fractions and mixed numbers in mathematics.

## What are the characteristics of proper fractions?

One of the main features of a proper fraction is that it always produces a decimal number that is less than one when divided. Another feature is that if the fraction is added to any whole number, the result will always be greater than one.

Furthermore, proper fractions often are represented in their simplest form, or in its reduced form, where the numerator and denominator have no common factors more than one. Finally, proper fractions can be converted to percentages or decimals to make it easier to calculate and compare with other numbers.

Some characteristics of fractions own are the following:

• Decimal value less than 1: As we mentioned earlier, the decimal value of a proper fraction is less than 1. For example, 3/4 has a decimal value of 0.75, which is less than 1.
• fractional part of a unit: Proper fractions represent a fractional part of a unit. For example, 2/3 represents two parts of a unit divided into three equal parts.
• Numerator less than denominator: The numerator of a proper fraction is always less than the denominator. If the numerator were equal to or greater than the denominator, it would be an improper fraction.
• always positive: Proper fractions are always positive, which means that their value is greater than zero. This is because the numerator and denominator are always positive numbers.
• can be simplified: Proper fractions can be simplified to their simplest form, dividing the numerator and denominator by their greatest common divisor. For example, the fraction 6/8 can be simplified by dividing both numbers by 2, leaving 3/4.

Proper fractions can be used in various mathematical equations and are essential for developing a strong understanding of mathematical concepts.

## How do you make a proper fraction?

To make a proper fraction, we simply need make sure the numerator is smaller than the denominator. For example, the fraction 2/3 is a proper fraction, since the numerator 2 is less than the denominator 3.

To make a proper fraction, the following steps must be followed:

• choose a numerator: The numerator is the number that goes above the horizontal line of the fraction. It must be an integer and can be positive or negative.
• choose a denominator: The denominator is the number that goes under the horizontal line of the fraction. Must be an integer and cannot be zero.
• Verify that the numerator is less than the denominator: For a fraction to be proper, the numerator must always be less than the denominator. If the numerator is equal to or greater than the denominator, the fraction will be improper.
• Simplify, if necessary: If the numerator and denominator have a common factor, they can be simplified by dividing by the same number. For example, if we have the fraction 10/20, it can be simplified by dividing both numbers by 10, remaining as 1/2.

We can also represent a proper fraction as a decimal dividing the numerator by the denominator. In the case of 2/3, the decimal equivalent is recurring 0.666. In short, to make a proper fraction, we need to make sure that the numerator is smaller than the denominator.

## What is the difference between proper and improper fractions?

In mathematics, fractions are represented by a numerator and a denominator, separated by a horizontal line. A proper fraction is a type of fraction where the numerator is smaller than the denominator.

In other words, the value of a proper fraction is less than one. For example, 1/3 and 4/5 are proper fractions, since the numerator is smaller than the denominator. Conversely, an improper fraction has a numerator that is equal to or greater than the denominator.

This type of fraction represents a value greater than one. For example, 5/3 and 8/7 are improper fractions, since the numerator is greater than the denominator. Understanding the difference between proper and improper fractions is important in various mathematical calculations, such as converting between fractions and mixed numbers, simplifying fractions, and comparing the value of fractions.

## What are proper fractions? – Examples

Proper fractions are important in mathematics, as they are one of the fundamental concepts entering primary school. In terms of features, a proper fraction can be defined as a fraction where the numerator is always less than the denominator.

For example, 1/2, 2/3 and 3/4 are examples of proper fractions. Proper fractions can also be represented in decimal form by dividing the numerator by the denominator, the resulting decimal being a value between 0 and 1.

Proper fractions are used in many different applications in mathematics, including fractions, decimals, percentages, ratios and dimensions.

Proper fractions play an essential role in mathematics and are fundamental to understanding more complex mathematical concepts, their value is less than 1 and they can be easily convert to decimal numbers.

Also, they are used in many real-world situations, such as calculating probabilities, measuring proportions, and making comparisons.