Mixed Numbers in everyday life

From everyday life you surely know another kind of fractions:

For example, the movie is one and three-quarters of an hour long, a bottle contains one and a half liters of water or your parents have walked six and a half kilometers.


The family party

Grandma baked 3 delicious cakes for the family party - three of Oliver's favourite cakes.

But they are not put on the table at the same time and even before the last two cakes are served, Oliver has devoured three pieces of the first cake and is well-fed...

There are 2 5/8 cakes left for the rest of the family.

This is called a mixed number or mixed fraction. A Mixed Fraction is a whole number and a proper fraction combined. Between the whole number and the fraction you can imagine a plus sign.

Definition: Mixed Number

A mixed number (or mixed fraction) is a short notation for the sum of the whole number and the following proper fraction:

2 5/8  =  2 + 5/8

Online Exercise: Naming Mixed Numbers

You can practice to name mixed numbers online:


What's an Improper Fraction?

The two cakes were cut into 8 equal pieces. Therefore each piece has the size of one eighth of a cake.

How many eighths (= pieces of cake) are there altogether?

Altogether there are 21/8 cakes.

Definition: Improper Fraction

A fraction whose numerator is greater than the denominator is called an improper fraction.

The example shows that an improper fraction can also be written as a mixed number (and vice versa):

2 5/8  =  21/8

The next two pages deal with the transformation of improper fractions and mixed numbers.

Video: What's a Mixed Number?

Finally, a video about: Introduction to Mixed Numbers:


Let's continue with:
Converting Mixed Numbers to Improper Fractions