Improper Fractions and Mixed Numbers

Main Learning Goal and Core Concepts: Students will learn what an improper fraction is and what a mixed number is. In addition, students will be able to convert improper fractions into mixed numbers and vice versa. This lesson assumes students already know how to compare fractions with the same denominators and how to simplify fractions.


Improper Fraction

A fraction with the numerator is larger than or equal to the denominator such as 2/2 or 3/2

Mixed Number

A number written as a whole number with a fraction; consists of a whole number and a proper fraction such as 1 1/2

Lesson Brief

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

  • We use long division in which we divide the numerator by the denominator.
  • We can ask ourselves: How many batches of an item can we fit into the whole group?

Example: What is the mixed number form of 11/2?

  • You can count the largest number of batches of 2 that goes into 11
  • 2 x 5 = 10 which is the largest number of batches of 2 that goes into 11
    • 5 is the whole number
  • You will see that 11 – 10 = 1 is left over, and you put the remainder of 1 over the original demoninator of 2 to get the fraction of 1/2
    • The mix number form of 11/2 is 5 1/2

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

  • We use multiplication and addition where we multiply the whole number with the denominator and add the numerator.
    • Note: The denominator remains the same during this conversion.
  • For example: 5 1/2 has the numerator as (5 x 2) + 1 = 11
    • You keep the same denominator of 2 and put the numerator over the demonminator → 11/2
      1. Multiply the whole number and denominator:
        • 5 x 2 = 10
      2. Add the numerator to the whole number, and then times the denominator:
        • 10 + 1 = 11
      3. Put the calculator number over the original denominator of 2:
        • 11/2


  • During these conversions it is important to keep the denominator the same. The only time the denominator would change would be if we were simplifying the improper fraction or mixed number before or after we convert. 

  • When converting, we always follow the order of operations. This is especially important when converting a mixed number to an improper fraction so that we can get the correct answer. 

  • When simplifying it is important to keep the whole number the same in a mixed number. We are simplifying the fraction, we are not changing the entire value of the mixed number.


‘Improper Fraction’ Definition: Source
Mixed Number’ Definition: Source 1, Source 2

If you would like a blank copy of the worksheet and the corresponding answer key, they can be found below:

Improper Fractions and Mixed Numbers- Converting, Comparing, and Simplifying

Improper Fractions and Mixed Numbers- Converting, Comparing, and Simplifying Answer Key