In mathematics, fractions correspond to a representation of parts of a whole. It determines the division of equal parts being that each part is a fraction of the whole.
As an example we can think of a pizza divided into 8 equal parts, with each slice corresponding to 1/8 (one eighth) of its total. If I eat 3 slices, I can say that I ate 3/8 (three-eighths) of the pizza.
It is important to remember that in fractions, the upper term is called numerator while the lower term is called denominator.
Types of Fractions
Own Fraction
They are fractions in which the numerator is smaller than the denominator, that is, it represents a number smaller than an integer. Ex: 2/7
Improper Fraction
They are fractions in which the numerator is greater, that is, it represents a number greater than the integer. Ex: 5/3
Apparent Fraction
They are fractions in which the numerator is multiple to the denominator, that is, it represents an integer written in the form of a fraction. Ex: 6/3 = 2
mixed fraction
It consists of an integer and a fractional part represented by mixed numbers. Ex: 1 2/6. (one integer and two sixths)
Note: There are other types of fractions, they are: equivalent, irreducible, unitary, egyptian, decimal, compound, continuous, algebraic.
You may also be interested in What is fraction?
Operations with Fractions
Addition
To add fractions it is necessary to identify whether the denominators are the same or different. If they are equal, just repeat the denominator and add the numerators.
However, if the denominators are different, before adding, we must transform the fractions into equivalent fractions of the same denominator.
In this case, we calculate the Least common multiple (MMC) between the denominators of the fractions we want to add, this value becomes the new denominator of the fractions.
Furthermore, we must divide the MMC found by the denominator and multiply the result by the numerator of each fraction. This value becomes the new numerator.
Examples:
Subtraction
To subtract fractions we have to be as careful as we do in the sum, that is, check if the denominators are equal. If so, we repeat the denominator and subtract the numerators.
If they are different, we do the same addition procedures, to obtain equivalent fractions of the same denominator, then we can do the subtraction.
Examples
Learn more at Addition and Subtraction of Fractions.
Multiplication
The multiplication of fractions is done by multiplying the numerators with each other, as well as their denominators.
Examples
Get more knowledge, read multiplication of fractions.
Division
When dividing between two fractions, the first fraction is multiplied by the inverse of the second, that is, the numerator and denominator of the second fraction are inverted.
Examples
Want to know more? read
- Multiplication and Division of Fractions
- Fraction Simplification
- Rationalization of Denominators
History of Fractions
The history of fractions goes back to Ancient Egypt (3,000 BC. C.) and reflects the need and importance for human beings about fractional numbers.
At that time, mathematicians marked their lands to delimit them. With that, in the rainy seasons the river crossed the limit and flooded many lands and, consequently, the markings.
Therefore, mathematicians decided to demarcate them with ropes in order to solve the initial problem of floods.
However, they noted that many plots were not made up of just whole numbers, there were plots that measured parts of that total.
It was from this that the geometers of the pharaohs of Egypt began to use fractional numbers. Note that the word Fraction comes from the Latin fracture and it means “party”.
check out Fraction Exercises who took the entrance exam and Mathematics in Enem.
Looking for texts on the topic for early childhood education? Find in: Fractions - Kids and Operation with Fractions - Kids.
