If you are searching for proper fractions and improper fractions then you landed on the correct page where you will get plenty of information on these concepts. In this article, you will know the definition of the fraction, Terminologies like Numerator and denominator, Proper fraction, improper fraction. Furthermore, you will find the steps on identifying the proper and improper fraction as well in the later modules.

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## Fraction – Definition

The fraction can be described as the part of the whole object. Fraction has the numerator and denominator separated by solidus. The numerator represents the total no of parts taken and the denominator represents how many parts the whole is divided into.

### Types of Fractions

Based on the numerator and the denominator, fractions are divided mainly into three types. They are 1.Proper fraction 2. Improper fraction 3. Mixed Fraction. In this article, we will mainly discuss the proper fraction and improper fraction.

### Proper Fraction

In a Proper fraction, the numerator is smaller than the denominator. Examples of the proper fraction are \(\frac { 2 }{ 5 } \), \(\frac {8 }{ 15 } \), \(\frac { 5 }{ 8 } \) etc.

The numerators are 2,8,5 and the denominators are 5, 15, 8.

Here the numerators 2,8,5 are less than the denominators 5, 15, 8.

Further simplification of the value of the proper fraction is always less than one and greater than zero.

### Improper Fraction

In an improper fraction, the numerator is greater than the denominator.Examples of an improper fraction are \(\frac { 8 }{ 3 }\), \(\frac { 9 }{ 5 } \),\(\frac { 3 }{ 2 } \),\(\frac { 15 }{ 4 } \),etc.

The numerators are 8,9,3,15 and the denominators are 3,5,2,4. Here the numerators 8,9,3,15 are greater than the denominators 3,5,2,4 etc.

Further simplification of the improper fraction gives the value equal to 1 and greater than one but not less than one.

By adding one or more whole numbers and one proper fraction we get an Improper fraction.

**Example:
**1+ \(\frac { 2 }{ 3 }\) =5/3

1+\(\frac { 2 }{ 7 }\)=9/7

By using this knowledge we can identify the proper fractions and improper fractions.

### How to Identify a Proper and Improper Fraction?

- If a fraction has a numerator less than the denominator then it is said to be a proper fraction. Fractions greater than 0 but less than 1 are called proper fractions.
- If a fraction has a numerator greater than or equal to the denominator then it is called an improper fraction. An improper fraction is 1 or greater than 1.

### Differences between Proper Fraction and Improper Fraction

Proper Fractions | Improper Fractions |
---|---|

In a Proper Fractions, the Numerator is less than the Denominator. |
In an improper fraction, the numerator is greater than the denominator. |

Examples of Proper fractions are 1/3,4/7,5/2,7/3, etc. | Examples of improper fractions are 3/2,6/2,8/3,9/4 etc. |

A rational Fraction N(x)/D(x)=>N(x) Degree is less D(x) degree is high | A rational fraction N(x)/D(x)=> N(x) Degree is high, D(x) degree is low |

The value of the proper fraction by further simplification is always less than one and greater than zero. | The value of the Improper fraction by further simplification is greater than one or equal to one but not greater than zero |

### FAQs on Proper Fraction

**1. What is Proper Fraction?
**In a Proper fraction, the numerator is less than the denominator.

**2. What is Improper Fraction?**

In an Improper Fraction, the numerator is greater than the denominator.

**3. What are the types of fractions?**

They are mainly three types of fractions. They are 1. Proper fractions 2. Improper fractions.3. Mixed fractions.

**4. What is the value of proper fraction after simplification?**

The value of the proper fraction after simplification is less than one and greater than zero.