In Mathematics, a fraction is described as the part of the whole. For instance, a burger is divided into four equal pieces, and then each piece is expressed as 1/6. Fractions or Partial Fractions help to distribute and estimate the numbers easily and make the calculation quicker. Instead of using decimal values, the representation of fractions seems simpler.

## Definition of Fraction

In mathematics, a fraction is used to denote the portion or the part of the whole thing. It describes the equal parts of the whole. A fraction has two parts, which are known as the numerator and the denominator. The number on the top is known as the numerator, and the number on the base is called the denominator. The numerator determines the number of equal parts taken, whereas the denominator represents the total number of equal parts in a whole.

For example, 2/12 is a fraction. Here, 2 is a numerator, and 12 is a denominator.

In real life, we have a few examples of fractions stated below:

- If a burger is divided into two equal parts, then every part is equal to half of the whole burger.
- If we divide a slice of cheese into three equal parts, then each part is similar to 1/3rd of the whole cheese.

### Types of Fractions

There are four main types of fractions.

- Unit Fraction – In a fraction, the numerator with the number 1 is called a unit fraction.For example, 1/5, 1/6.
- Proper Fraction – If the numerator value is less than the denominator value, it is known as a proper fraction. Example: 8/9, 4/10
- Improper Fraction – If the numerator value is greater than the denominator value, then it is known as an improper fraction. Example: 9/5, 10/15
- Mixed Fraction – If a fraction includes a whole number with a proper fraction, it is called a mixed fraction. Example 8 2/5, 6 5/8

## What is a Partial Fraction?

An algebraic fraction that can be divided into simpler parts is known as partial fractions. The simpler parts of algebraic fractions are known as partial fractions.

### Partial Fraction Formula:

The method or the formula for determining the partial fraction breakdown is explained with the assistance of the steps given below-

Step 1: In the process of decomposing the rational expression into the partial fraction, one should begin with the proper rational expression.

Step 2: Now, factor the given denominator of the rational expression into the linear factor or in the form of basic quadratic factors

Step 3: Then write down the partial fraction for each of the respective factors obtained, with the variables in the numerators, name them X and Y.

Step 4: To find the variable values of X and Y, multiply the whole equation by the respective denominator.

Step 5: Solve for the variables by replacing zero in the factor variable.

Step 6: Lastly, replace the values of X and Y in the partial fractions.

## FAQs

**What are the various denominator types in the partial fractions?**

The four different types of denominator observed in the partial fractions are:

Linear factors

Repeated linear factors

Irreducible factors of degree 2

Repeated irreducible factors of degree 2

**What is the advantage of partial fraction decomposition?**

Partial fraction decomposition is done to find the inverse place transformation and help integrate and help the rational functions.

**What is indicated by proper and improper rational expressions?**

In proper rational expression, the value of the numerator is less than the value of the denominator. Whereas in improper rational expression, the numerator’s value is greater than the value of the denominator.

## Conclusion

Fractions are an integral part of mathematics. Fractions help in the basic understanding of complex number equations and operations. Understanding the basics of fractions is very important. Fractions will allow students to advance and excel in their academics. Cuemath is an online learning platform that enables you to understand fractions in detail. With the help of Cuemath interactive worksheets, you can master the concept of fractions in a fun and exciting way.

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