## Definition of Proper Fractions

When the **numerator** is less than the denominator, it is called a ** Proper function**.

- If you want to describe a part of a whole, it is called a Fraction.
- Denominator – The number on the bottom of the fraction and it shows the number of equal parts, where the whole is divided into.
- Numerator – The numerator is the number on the top of the fraction, and it shows the number of the parts we are considering.
- Example, in the fraction 5/6, it shows “5 of 6 equal parts.” 5 is the numerator, and 6 is the denominator.

**Example of a Proper Fraction**:

*numerator*less than 6, which is the denominator.

Few more Proper Fraction examples are :

\(\frac{1}{9} , \frac{2}{7}, \frac{4}{9}\).**Note:** In all the above examples, the number on the top (numerator) is smaller than the number at the bottom(denominator).

So, basically, it is a way to divide or cut any object in smaller parts. Example, if you divide a bar of chocolate into two equal parts, it would be called as* two halves.*

It can be denoted mathematically as

\(\frac{1}{2} +\frac{1}{2}= 1\)This expression is called a **Fraction. **You may divide the chocolate bar into more pieces too.

## Types of fractions:

There are 3 types of fractions, and an overview of them is given below:

Types of Fractions |
Proper Fractions / Common Fractions |
Improper Fractions |
Mixed Fractions |

Property |
In this, the numerator is smaller than the denominator. | In this, the numerator is larger or equal than the denominator. | It’s a combination of a whole number and a proper fraction. |

Example |
\(\frac{2}{3}\) | \(\frac{2}{1} or \frac{5}{5}\) | \(5\frac{1}{2}\) |

** Point to know – **If the numerator and denominator of a fraction are multiplied by the same number, its value doesn’t change.

Let’s Solve a few problems on Propper fractions:

Question |
Answer |

Is \(\frac{1}{2}\) a proper fraction? | Yes, It is a proper fraction because the numerator 1 in this fraction is less than the denominator 2. |

Is \(\frac{4}{2}\) a proper fraction? | No, It is not a proper fraction because the numerator 4 in this fraction is more than the denominator 2. It is an improper fraction. |

Is \(\frac{9}{8}\) a proper fraction? | No, It is not a proper fraction because the numerator 9 in this fraction is more than the denominator 8. It is an improper fraction. |

Is \(\frac{6}{5}\) a proper fraction? | No, It is not a proper fraction because the numerator 6 in this fraction is more than the denominator 5. It is an improper fraction. |

Is \(\frac{5}{9}\) a proper fraction? | Yes, It is a proper fraction because the numerator 5 in this fraction is less than the denominator 9. |