Types of Fractions

1. What are the different types of fractions?

There are 3 different types of fractions:
  1. Proper fractions
  2. Improper fractions
  3. Mixed numbers or mixed fractions

2. What are Proper Fractions?

In a proper fraction, the numerator (top number) is smaller than the denominator (bottom number).

Examples:
3
4
 , 
4
5
 , 
12
17
 ,  etc.

square metre or square meter

3. What are Improper Fractions?

In an improper fraction, the numerator (top number) is bigger than or equal to the denominator (bottom number).

Examples:
4
3
 , 
6
5
 , 
10
7
 , 
4
4
 ,  etc.

square metre or square meter

4. What are Mixed Numbers or Mixed Fractions?

A mixed number is made up of two parts - a whole number and a proper fraction.

Examples:
5 2
3
 , 
1 1
4
 , 
3 5
12
 , 
2 1
2
 ,  etc.

square metre or square meter

Notes:

  • Improper fractions can be converted to mixed numbers and mixed numbers can be converted back to improper fractions. Improper fractions and mixed numbers are 2 different ways to represent the same number.

  • Improper fractions are useful when writing mathematical formulae. Compared to a mixed number, it's easier to write, use and operate upon a number written as an improper fraction and not be confused.

  • Mixed numbers have their utility when talking about quantities in day-to-day life. For example, you say,
    "I need
    2 1
    2
    cups of sugar for the cake."
    instead of
    "I need
    5
    2
    cups of sugar for the cake."


    Although they both mean the same amount of sugar,
    2 1
    2
    cups of sugar makes more sense than
    5
    2
    cups of sugar.