Types of Fractions

The various types of fractions are:

1. Like Fractions:

The fractions having the same denominators are known as like fractions.

We know that fractions such as 2/5, 3/5, 5/5, 7/5, 9/5, ….etc., are like fractions.

2. Unlike Fractions:

Fractions having different denominators are called unlike fractions.

$\frac{3}{5}$, $\frac{2}{7}$, $\frac{5}{9}$, $\frac{4}{11}$, ......... are unlike fractions.

3. The same Numerator Fractions:

The factors having the same numerators are called the same numerator fractions.

Fractions such as 2/5, 2/7, 2/9, 2/11, …………, etc., are same numerator fractions.

4. Unit Fractions:

The fractions having one (1) as their numerator are called unit fractions.

1/3, 1/5, 1/7, 1/9, …………, etc., are unit fractions.

5. Proper Fractions:

A fraction in which the denominator is greater than the numerator is called a proper fraction. We can also say that a fraction with its numerator less than the denominator is known as a proper fraction.

1/2, 2/3, 4/5, 5/6, 7/10, 9/11, 11/21, 35/45, ……….., etc., are proper fractions.

A fraction in which numerator is less than its denominator.

[$\frac{3}{4}$, $\frac{5}{7}$, $\frac{11}{17}$ ...............]

Observe the following number line.

$Types of Fractions - Number Line$

Consider the fraction $\frac{5}{8}$

It lies between 0 and 1 and its numerator is less than the denominator.

Fractions in which numerators are smaller than the denominators are called proper fractions.

6. Improper Fractions:

A fraction in which the denominator is smaller than or equal to its numerator is called an improper fraction. We can also say that a fraction with its numerator greater than or equal to the denominator is known as an improper fraction.

5/3, 9/5, 11/7, 17/8, 21/14, 19/15, …….., etc., are improper fractions.

A fraction in which numerator is equal to or greater than its denominator.

[$\frac{15}{7}$, $\frac{24}{13}$, $\frac{5}{5}$ ...............]

$Types of Fractions - Number Line$

Consider the fraction $\frac{10}{8}$

It is greater than one and its numerator is greater than the denominator.

Fractions in which numerators are greater than the denominators are called improper fractions.

The fraction $\frac{8}{8}$ = 1, similarly $\frac{3}{3}$ = 1, $\frac{7}{7}$ = 1, $\frac{11}{11}$ = 1 .............

Fractions in which numerators are equal to the denominators are also called improper fractions.

7. Mixed Fractions:

When an improper fraction is written as a combination of a whole number and a proper number, it becomes a mixed fraction or mixed number.

As: 6/5 = 5 + 1/5 = 5/5 + 1/5 = 1 + 1/5 = 1$\frac{1}{5}$

1$\frac{1}{2}$, 1(\frac{1}{4}\), 2(\frac{3}{4}\), 3(\frac{5}{7}\), 5(\frac{1}{9}\), ……….., etc., are mixed fractions.

(All types of fraction may be categorized into three kinds, i.e., proper, improper and mixed fraction).

Mary ate 2 apples and Kerry ate $\frac{1}{2}$ of an apple. They are 2 and $\frac{1}{2}$ apples together.