A fraction describes a part of a whole. The number on the bottom of the fraction is called the denominator, and it denotes how many equal parts the whole is divided into. The number on the top of the fraction is called the numerator, and it denotes how many of the parts we are taking. For example, the fraction 3/4 denotes "3 of 4 equal parts." 3 is the numerator, and 4 is the denominator.

A proper fraction is a fraction whose numerator is smaller than its denominator. An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 3/4, 2/11, and 7/19 are proper fractions, while 5/2, 8/5, and 12/11 are improper fractions.

A mixed number is composed of a whole number and a fraction. 6 2/3, 18 5/4, and 2 2/5 are all mixed numbers.

Improper fractions can also be represented as a mixed number. To convert an
improper fraction into a mixed number, divide the numerator by the denominator.
The resultant becomes the whole number, and the remainder becomes the numerator
of the new fraction. The denominator of the new fraction is the same as the
original denominator. If there is no remainder, then there is no fraction--the
result is simply a whole number.

For example, we can convert 48/5 into a mixed number:

48/5 = 9
, with a remainder of 3. Thus, 48/5 = 9 3/5.

To convert a mixed number into an improper fraction, multiply the whole number
by the denominator and add it to the numerator. This becomes the numerator of
the improper fraction; the denominator of the new fraction is the same as the
original denominator.

For example, we can convert 9 3/5 into a mixed number:

9×5 = 45
, and
45 + 3 = 48
. Thus, 9 3/5 = 48/5.