A mixed numeral (also called a mixed fraction or mixed number) is a traditional denotation of the sum of a non-zero integer and a proper fraction (having the same sign). It is used primarily in measurement: inches, for example.

Video: Improper fraction

Scientific measurements almost invariably use decimal notation rather than mixed numbers. The sum is implied without the use of a visible operator such as the appropriate "+". For example, in referring to two entire cakes and three quarters of another cake, the numerals denoting the integer part and the fractional part of the cakes are written next to each other as instead of the unambiguous notation Negative mixed numerals, as in , are treated like Any such sum of a whole plus a part can be converted to an improper fraction by applying the rules of adding unlike quantities.

This tradition is, formally, in conflict with the notation in algebra where adjacent factors denote a product, without an explicit infix operator. When two algebraic expressions are written next to each other, the operation of multiplication is implied by this general rule: always means the product of and , even if the value of is a fraction. The expression for example is not a mixed number, instead, multiplication is expressly required, where

For better readability, the multiplication is sometimes made explicit or parentheses are added. So, may be written as

or or

How do you convert an improper fraction into a mixed number?

Video: Convert improper fraction into a mixed number

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 .