In a Proper fraction, the numerator usually gives us an idea of how many parts of the denominator we are going to use, while the denominator is the total number of parts we have.

A good way to remember the term proper fraction is to start thinking that this is the best way to work with fractions in general. In proper fractions, the top number or the numerator is smaller than the bottom number or the denominator.

Proper Fraction and Improper Fraction

$\frac{1}{2}$ Is proper fraction compared to $\frac{2}{1}$

Proper fraction is one where the numerator or the number on top is less than the denominator or the number at the bottom and the overall value is less than 1.

Proper Fraction

Examples: $\frac{4}{9}$, $\frac{2}{5}$, $\frac{15}{16}$, $\frac{5}{6}$

In the above example, the numerator (top number) is less than the denominator (bottom number).

We can also explain proper fractions by saying that it is not proper to allow a bigger number to sit on top of an smaller number so for a proper fraction to work it is advisable to put the smaller number on top.

Let us try some of these now..

Proper Fraction Example

How do I write a proper fraction?

The word fraction would tell us a part of something and it represents a type of numeral. In most of cases, the quotient of two integers with of course the top number being called the numerator which we sometimes denote as (the number of parts), and the bottom number being the denominator (how many parts the whole is divided into). These when written out, the numerator and the denominator would be separated by "/" or "_".

Usually we denote a fraction by $\frac{a}{b}$ in which both "a" and "b" are the whole numbers and "b" is not equal to zero.

Any rational number between zero and 1 can be represented by fractions and if the quotient is less than one, such as $\frac{1}{5}$ or $\frac{2}{7}$, then it is called a proper fraction.

Anything other than this representation would be considered as an improper where the quotient is greater than one or in other words if the numerator of a fraction is larger than the denominator such as $\frac{18}{8}$

Can a fraction's numerator be equal to zero?
In the context of division we have learned that it is not possible or proper to be divided by zero, which is categorized as undefined.
But we do can have zero as our numerator and any fraction with zero as numerator would result in zero so all the fractions like $\frac{0}{2}$, $\frac{0}{450}$, $\frac{0}{29}$ equal zero.