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There are 3 different types of fractions:

- Proper fractions
- Improper fractions
- Mixed numbers or mixed fractions

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

*Example:*

3

4, 4

5, 12

17, etc.

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

*Example:*

4

3, 6

5, 10

7, 4

4, etc.

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

*Example:*

5 2

3, 1 1

4, 3 5

12, 2 1

2, etc.

- 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__

2cups of sugar for the cake" instead of "I need __5__

2cups of sugar for the cake". Although they both mean the same amount of sugar, 2 __1__

2cups of sugar makes more sense than __5__

2cups of sugar.