Mixed Number Mania!

Contributor: Erika Wargo. Lesson ID: 12823

Let's see: Pizzas come in 8 slices. After the party, we had 18 slices left. How many pizzas are there? This problem requires mixed (not mixed-up!) numbers -- fractions and whole numbers! Easy enough!


Fractions and Operations

learning style
personality style
Grade Level
Intermediate (3-5)
Lesson Type
Skill Sharpener

Lesson Plan - Get It!


After a party with your friends, there are three full pizzas and one-half pizza left. How do you write that as a mixed number?

A whole number combined with a fraction is called a mixed number.

A mixed number has two parts: the whole number and the fraction.

“One and one-third” would be written as:

“Two and three-eighths” would be written as:

“Twenty-one and four-fifths” would be written as:

Do you see how in each example the mixed number is made up of a whole number and a proper fraction together? A mixed fraction or a mixed number is a mix of a whole number and a fraction!

The parts of a mixed number have specific names:

The “3” is the whole number. The whole number, 3, is represented by three whole circles as shown below.

The “1” in the fraction is the numerator. The “2” in the fraction is the denominator. The last circle is divided into two equal parts, with one of the parts shaded in:

fraction diagram

When naming mixed numbers, use the word “and” in between the whole number and the fraction. In the example above, it would be read as “three and one-half.”

Mixed numbers can also be rewritten as improper fractions to show an equivalent amount. An improper fraction is a fraction where the numerator is greater than or equal to the bottom number. To write a mixed number as an improper fraction, count the fractional parts.

fraction diagram

Count all of the halves. There are seven halves shaded in, so 3½ can also be written as 72.

Most of the time, you will not have fraction diagrams to look at. To convert a mixed fraction to an improper fraction:

  1. Multiply the whole number part by the denominator of the fraction: 3 x 2 = 6.
  2. Add that value to the numerator of the fraction: 6 + 1 = 7.
  3. Write the result as the numerator of an improper fraction and keep the denominator the same. The improper fraction is “seven halves” or

Improper fractions are needed when performing operations with mixed numbers, such as multiplication and division.

Take a moment to review fractions and mixed numbers with Shmoop’s video, Improper Fractions and Mixed Numbers by Shmoop:


After the video, discuss with a parent or teacher how to identify the difference between a proper fraction, an improper fraction, and a mixed number by the way each is written. What is special about the numerator and denominators of each?

Now you will practice writing and mixed numbers in the Got It? section with interactive practice and games.

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