**Definition**

Part of a whole.A number written with the bottom part (the denominator) telling you how many parts the whole is divided into, and the top part (the numerator) telling how many you have.

Here 3 –numerator , 7 –denominator.

### Proper and improper common fractions

A common fraction is said to be a **proper fraction** if the absolute value of the numerator is less than the absolute value of the denominator—that is, if the absolute value of the entire fraction is less than 1. A vulgar fraction is said to be an **improper fraction** if the absolute value of the numerator is greater than or equal to the absolute value of the denominator.

### Mixed numbers

A **mixed numeral** (often called a *mixed number*, also called a *mixed fraction*) is the sum of a whole number and a proper fraction. This sum is implied without the use of any visible operator such as “+”. For example, in referring to two entire cakes and three quarters of another cake, the whole and fractional parts of the number are written next to each other:

An improper fraction is another way to write a whole plus a part. A mixed number can be converted to an improper fraction as follows:

1. Write the mixed number as a sum .

2. Convert the whole number to an improper fraction with the same denominator as the fractional part, .

3. Add the fractions. The resulting sum is the improper fraction. In the example, .

Similarly, an improper fraction can be converted to a mixed number as follows:

- Divide the numerator by the denominator. In the example, , divide 11 by 4. 11 ÷ 4 = 2 with remainder 3.
- The quotient (without the remainder) becomes the whole number part of the mixed number. The remainder becomes the numerator of the fractional part. In the example, 2 is the whole number part and 3 is the numerator of the fractional part.
- The new denominator is the same as the denominator of the improper fraction. In the example, they are both 4. Thus .