Home > Pre-algebra > Fractions > Improper And Mixed Numbers

## Improper And Mixed Numbers

#### Introduction

Traditional fractions are usually written with a lower numerator and higher denominator. An improper fraction is one where the denominator is higher than the numerator. A mixed fraction (or mixed number) is when a whole number is combined with a fraction.

#### Terms

Fraction - Fractions are used when using numbers to express parts of whole.
Improper Fraction - A fraction where the numerator is greater than the denominator.
Mixed Fraction - A fraction where a whole number is combined with a fraction.
Numerator - The top part of the fraction, referring to the parts taken from the whole.
Denominator - The bottom part of the fraction, referring to the number of parts that make up the whole.
Whole Number - A whole number is a number with nothing but zeroes after the decimal point.

## Lesson

An improper fraction can always be expressed as a mixed fraction. If we are given , we need to perform the division and then write the answer as a mixed fraction.

So (with 3 as the remainder) – this can be written as

Similarly, if we are given a mixed fraction and asked to express it as a improper fraction, we multiply the whole number by the denominator and add the numerator. The result becomes the new numerator and the denominator remains the same.

So in the case of , the whole number is first multiplied by the denominator (1*3) then added to the numerator (3+1). The final result is .

## Examples

#### Write Improper Fraction as Mixed Number (Example #1)

Write as a mixed number
Because is an improper fraction (the numerator is greater than the denominator), we need to convert it to a mixed number

#### Write Mixed Number as Improper Fraction (Example #1)

Write as an improper fraction

#### Write Improper Fraction as Mixed Number (Example #3)

Write as a mixed number
Because is an improper fraction (the numerator is greater than the denominator), we need to convert it to a mixed number

#### Write Mixed Number as Improper Fraction (Example #2)

Write as an improper fraction