Proper fraction:
A proper fraction is a fraction where the numerator is less than the denominator. In other words, the value of the fraction is less than 1. Proper fractions are often used to represent parts of a whole or parts of a set.

Example:
- 2/3 is a proper fraction. The numerator (2) is less than the denominator (3), so it is a proper fraction. This fraction represents two out of three equal parts.

Improper fraction:
An improper fraction is a fraction where the numerator is greater than or equal to the denominator. The value of an improper fraction is always greater than or equal to 1.

Example:
- 5/3 is an improper fraction. The numerator (5) is greater than the denominator (3), so it is an improper fraction. This fraction represents five out of three equal parts.

Mixed fraction:
A mixed fraction is a combination of a whole number and a proper fraction. It is written as a whole number followed by a proper fraction.

Example:
- 2 1/4 is a mixed fraction. The whole number part is 2 and the proper fraction part is 1/4. This mixed fraction represents two whole units and one-fourth of another unit.

Unit fraction:
A unit fraction is a fraction where the numerator is 1 and the denominator is a positive integer. Unit fractions represent equal parts of a whole or a set.

Example:
- 1/5 is a unit fraction. The numerator (1) is 1 and the denominator (5) is a positive integer. This fraction represents one-fifth of a whole or a set.

Therefore, out of the given options, the type of fraction that has the numerator less than the denominator is a proper fraction (option A).