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Editor’s collection of notes:

Pre-Algebra

Fraction, Proper and Improper

 

 

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from https://www.mathsisfun.com/improper-fractions.html

 

pie 4/4pie 3/4
7/4
(seven-fourths or seven-quarters)

 

An Improper Fraction has a top number larger than (or equal to) the bottom number.

It is usually "top-heavy"

 

More Examples

3/2 7/3 16/15 15/15 100/5

See how the top number is bigger than (or equal to) the bottom number That makes it an Improper Fraction.

 

Three Types of Fractions

Fraction Types: Proper, Improper, Mixed

A Fraction (such as 7/4) has two numbers:

Numerator

Denominator

The top number (the Numerator) is the number of parts we have.
The bottom number (the Denominator) is the number of parts the whole is divided into.

Example: 7/4 means:

  • We have 7 parts
  • Each part is a quarter (1/4) of a whole

 

So we can define the three types of fractions like this:

Proper Fractions: The numerator is less than the denominator
Examples: 1/3, 3/4, 2/7
   
Improper Fractions: The numerator is greater than (or equal to) the denominator
Examples: 4/3, 11/4, 7/7
   
Mixed Fractions: A whole number and proper fraction together
Examples: 1 1/3, 2 1/4, 16 2/5

 

So an improper fraction is a fraction where the top number (numerator) is greater than or equal to the bottom number (denominator): it is top-heavy.

 

4/4
4/4

Can be Equal

What about when the numerator is equal to the denominator? For example 4/4 ?

Well it is the same as a whole, but it is written as a fraction, so most people agree it is a type of improper fraction.

We can use either an improper fraction or a mixed fraction to show the same amount.

For example 1 3/4 = 7/4, as shown here:

 

1 3/4   7/4
pie fullpie 3/4 = pie 4/4pie 3/4