There are several definitions for fractions, which are used according to the didactic needs of the target audience. The most used are:
One fraction is the representation of one or more parts of something that has been divided equally;
One fraction represents a division, where the numerator equals the dividend and the denominator equals the divisor;
a fraction is a rational number.
All of these definitions are correct and all of them will be explained later in this article.
Fractions: Parts of an integer
Any “original object” that has not been split is called an integer. By making cuts on this object, we are dividing it. If the division result in equal parts, you can represent this object through fractions. The following image represents an apple that has been divided into four equal parts.
THE fraction which represents one of these four parts is as follows:
1
4
This fraction should be read as follows: a bedroom.
THE fraction which represents the whole apple, which has been divided into four equal parts, is as follows:
4
4
This fraction should be read as follows: Four rooms.
At fractions must be named from this logic up to the denominator 10. From the denominator 11, we have: 11th, 12th... For example:
1
12
This fraction is one twelfth.
the top of a fraction – which represents the parts in question of an object that has been divided into equal parts – is equivalent to the dividend of a division and is called a numerator. The bottom part – which represents the number of parts into which an object was divided – is equivalent to the divisor of a division and is called dividend.
Fractions: rational numbers
The set of rational numbers is composed of any number that can be written in the form of fraction. Thus, the representatives of this group are as follows:
Any whole number;
Any finite decimal number;
Any periodic decimal (All periodic decimals can be written in the form of fraction. For this, we suggest reading the text generating fraction).
Equivalent fractions and simplification
equivalent fractions are those that represent the same rational number. This means they have the same value. For example:
4 = 8
2 4
Both fractions represent the integer 2.
To find equivalent fractions, just multiply numerator and denominator of a fraction by the same number (it can be any number, unless the problem requires something specific). For example:
3·4 = 12
7·4 28
As numerator and denominator were multiplied by the same number, the fractions three sevenths and twelve twenty-eighths are equivalent.
The process of division by the same number can also be used to find equivalent fractions. When this process is used, we say that the fraction was simplified. For example:
36:12 = 3
48:12 4
If the result of simplification is a fraction that can no longer be simplified, it will be called irreducible fraction.
Operations with fractions
Multiplication of fractions:
to multiply fractions, just multiply numerator by numerator and denominator by denominator. For example:
2·3 = 6
4 9 36
Division of fractions:
For split fractions, rewrite the division as a multiplication keeping the first fraction intact and inverting the numerator and denominator of the second. For example:
2:3 = 2·9 = 18
4 9 4 3 12
- Addition and subtraction of fractions:
If the fractions have equal denominators, just add (or subtract) the numerator as the exercise indicates. For example:
2 + 3 = 2 + 3 = 5
3 3 3 3
If fractions have different denominators, it is necessary to find equivalent fractions to them that have equal denominators to add them later. The procedure for this can be found on here.
By Luiz Paulo Moreira
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/o-que-e/matematica/o-que-e-fracao.htm
