What is a Fraction?
Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator. It shows the total number of equal parts the whole is divided into or the total number of the same objects in a collection.
Fraction, in arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.
In a proper fraction, the numerator is less than the denominator. If the numerator is greater, it is called an improper fraction and can also be written as a mixed number—a whole-number quotient with a proper-fraction remainder.
Any fraction can be written in decimal form by carrying out the division of the numerator by the denominator. The result may end at some point, or one or more digits may repeat without end.
The word fraction is derived from the Latin word “fractio” which means ‘to break’. The Egyptians, being the earliest civilization to study fractions, used fractions to resolve their mathematical problems, which included the division of food, supplies, and the absence of a bullion currency.
In Ancient Rome, fractions were only written using words to describe a part of the whole. In India, the fractions were first written with one number above another (numerator and denominator), but without a line. It was the Arabs only, who added the line which is used to separate the numerator and the denominator.
Different Types of Fractions
There are in total six types of fractions such as:
- Proper fraction.
- Improper fraction.
- Mixed fraction.
- Like fractions.
- Unlike fractions.
- Equivalent fractions.
The relationship between each different denominator and each different numerator determines what kind of fraction it is.
Let’s take a look at the different types of fractions.
In this type of fraction, the numerator is smaller than the denominator:
Like 1/3, 2/3, 5/7
The quotient, or division, of a proper fraction will always result in a value less than one.
This is a fraction where the numerator is larger than the denominator:
Like 3/2, 4/3, 7/4
Because the value of the numerator is larger, the quotient of an improper fraction will always result in a value greater than or equal to 1.
This type of fraction occurs when you combine a natural number and a fraction:
A mixed fraction can be converted into an improper fraction by multiplying the whole number by the denominator and adding the numerator. The resulting number will serve as a numerator over the original denominator:
7×3 = 21
Because mixed fractions have a whole number part, they are greater than the value of 1.
If the denominators of two or more fractions are the same, then they are called like fractions. For example, 1/6, 2/6, 3/6, 5/6, are known as like fractions. We can perform addition and subtraction of fractions only on like fractions. In some cases, we need to convert unlike fractions to like fractions to add or subtract.
If the denominators of two or more fractions are different, then the fractions are termed as unlike fractions. For example, 1/2, 1/3, 2/5, 3/6, etc. If the fractions are unlike, while adding or subtracting the fractions, we convert them to like fractions.
Equivalent fractions are the fractions that have different numerators and different denominators but are equal to the same value when simplified or reduced. For example, 2/4, 3/6, 4/8 are all equivalent fractions because they all get reduced to 1/2.
Apart from these, there are fractions with 1 as the numerator. Let us read about them.
Units fractions are those fractions in which the numerator is 1 and the denominator is a positive integer. For example, 1/3, 1/8, 1/19, 1/23, and so on are called unit fractions.