
Classifying Fractions 

Unit 14 > Lesson 2 of 11 
Look at each fraction
below. How are these fractions similar? How are they different?

The fractions above are similar since each one has a denominator of 4. Look at the circles below to see how these
fractions are different.

The fraction
is called a proper fraction. The fractions
and are improper fractions.

Definition: 
A proper fraction is a fraction in which the
numerator is less than the denominator. 
Definition: 
An improper fraction is a fraction in which the
numerator is greater than or equal to the denominator. 
In example 1, we will identify each fraction as proper or improper. We will
also write each fraction using words.

Example 1

Fraction 
Type 
Words 

improper 
threehalves 

proper 
twofifths 

improper 
threethirds 

proper 
fivesixths 

improper 
eleveneighths 

improper 
eighteighths 
What do the fractions in example 2 have in common?

Example 2 


twohalves 



threethirds 



fourfourths 



fivefifths 



sixsixths 

In example 2, each fraction has a numerator that is equal to its denominator. Each of these fractions
is an improper fraction, equal to one whole (1). An improper fraction can also be greater than one
whole, as shown in example 3.

Example 3



In the improper fraction sevenfourths, the numerator (7) is greater than the denominator (4). We can
write this improper fraction as a mixed number.

Definition: 
A mixed number consists of a wholenumber part and a
fractional part. 
In examples 4 through 6, we will write each improper fraction as a mixed number.

Example 4 



In example 4, sevenfourths is an improper fraction. It is really the sum of fourfourths and
threefourths. Sevenfourths is written as the mixed number one and
threefourths, where one is the wholenumber part, and threefourths
is the fractional part.

Example 5




In example 5, the improper fraction seventhirds is written as the mixed number two and
onethird, where two is the wholenumber part, and onethird is
the fractional part.

In example 6, the improper fraction seventeenfifths is written as the mixed number three and
twofifths, where three is the wholenumber part, and twofifths
is the fractional part.

In example 7, we will write each number using words. We will then classify each number as a proper fraction, an improper
fraction, or a mixed number. Place your mouse over the answer text see if you got it right.

Example 7

Number 
Words 
Type of Fraction 

threeeighths 
answer
1 

one and threesevenths 
answer
2 

fivefifths 
answer
3 

elevenfourths 
answer
4 

three and fivesixths 
answer
5 

eightthirds 
answer
6 

fourteensevenths 
answer
7 
The last number in example 7 can be written as a whole number: fourteensevenths is equal to two
wholes (2).

How can you tell if a fraction is less than 1, equal to 1, or greater than 1?

Compare the numerator and denominator 
Example 
Type of Fraction 
Write As 
If the numerator < denominator, then the fraction < 1. 

proper fraction 
proper fraction 
If the numerator = denominator, then the fraction = 1. 

improper fraction 
whole number 
If the numerator > denominator, then the fraction > 1. 

improper fraction 
mixed number 
Summary: 
A number can be classified as a proper fraction, an improper fraction, or as a mixed
number. Any number divided by itself is equal to one. A mixed number consists of a wholenumber part
and a fractional part.

Exercises
In Exercises 1 through 5, click once in an ANSWER BOX and type in your answer;
then click ENTER. After you click ENTER, a message will appear in the RESULTS
BOX to indicate whether your answer is correct or incorrect. To start over,
click CLEAR. Note: To write the fraction twothirds, enter 2/3 into the
form.

1. 
Write a proper fraction using only the digits 7 and 2.




2. 
Write an improper fraction using only the digits 5 and 8.




3. 
Write twelvesixths as a whole number.




4. 
Write one and twothirds as an improper fraction.




5. 
Write one and onefourth as an improper fraction.




This lesson is by Gisele Glosser. You can find me on Google.
