Any simple fraction consists of two numbers – the numerator and the denominator. The quantity that occurs above the slash is known as the numerator and the quantity that occurs below the slash is known as the denominator.

For example, consider the fraction \frac{7}{9}. Here, 7 is the numerator of the fraction, and 9 is the denominator of the given fraction.

**Numerator Greater than Denominator:**

If the value of the numerator is greater than the denominator then the fraction is known as an improper fraction. Some examples of such fractions are,

- \frac{13}{9}.
- \frac{14}{5}.
- \frac{67}{19}.

Note that **if the numerator is greater than the denominator** (that is, the denominator is less than the numerator)** then the value of the fraction is always greater than one.**

This can also be seen from the above examples by converting them into decimal fractions by long division. Note that all of the improper fractions below have values greater than one.

- \frac{13}{9} = 1.4444
- \frac{14}{5} = 2.8
- \frac{67}{19} = 3.5263

**Numerator Less than Denominator:**

If the value of the numerator is less than the denominator (that is, the denominator is greater than the numerator) then the fraction is known as a proper fraction. Some examples of such fractions are,

- \frac{4}{9}.
- \frac{14}{20}.
- \frac{7}{18}.

Note that **if the numerator is less than the denominator then the value of the fraction is always less than one.**

This can also be seen from the above examples by converting them into decimal fractions by long division. Note that all of the improper fractions below have values greater than one.

- \frac{4}{9} = 0.4444
- \frac{14}{20} = 0.7
- \frac{7}{18} = 0.3889