Improper Fractions


An Improper fraction has a top number
larger than (or equal to) the bottom number,

It is "top-heavy"

(seven-fourths or seven-quarters)

More Examples

3   7   16   15   99
2   3   15   15   5

See how the top number is bigger than (or equal to) the bottom number?
That makes it an Improper Fraction, (but there is nothing wrong about Improper Fractions).

Three Types of Fractions

There are three types of fraction:

Fraction Types


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


The top number is the Numerator, it is the number of parts you have.
The bottom number is the Denominator, it 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

Improper Fraction

So, an improper fraction is just a fraction where the top number (numerator) is greater than or equal to the bottom number (denominator).

In other words, it is top-heavy.


Can be Equal

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

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

Improper Fractions or Mixed Fractions

You can use either an improper fraction or a mixed fraction to show the same amount. For example 1 3/4 = 7/4, shown here:

1 3/4   7/4


Converting Improper Fractions to Mixed Fractions

To convert an improper fraction to a mixed fraction, follow these steps:

  • Divide the numerator by the denominator.
  • Write down the whole number answer
  • Then write down any remainder above the denominator.

Example: Convert 11/4 to a mixed fraction.


11 ÷ 4 = 2 with a remainder of 3

Write down the 2 and then write down the remainder (3) above the denominator (4), like this:

2 3


Converting Mixed Fractions to Improper Fractions

To convert a mixed fraction to an improper fraction, follow these steps:

  • Multiply the whole number part by the fraction's denominator.
  • Add that to the numerator
  • Then write the result on top of the denominator.

Example: Convert 3 2/5 to an improper fraction.

Multiply the whole number by the denominator:

3 × 5 = 15

Add the numerator to that:

15 + 2 = 17

Then write that down above the denominator, like this:


Are Improper Fractions Bad ?

NO, they aren't bad!

For mathematics they are actually better than mixed fractions. Because mixed fractions can be confusing when you write them down in a formula (are the two parts supposed to be added or multiplied?):

Mixed Fraction: What is: 1 + 2 1/4   ?
  Is it: 1 + 2 + 1/4   = 3 1/4 ?
  Or is it: 1 + 2 × 1/4   = 1 1/2 ?
Improper Fraction: What is: 1 + 9/4   ?
  It is: 4/4 + 9/4 = 13/4   yes

But, for everyday use, people understand mixed fractions better.

Example: It is easier to say "I ate 2 1/4 sausages", than "I ate 9/4 sausages"

We Recommend:

  • For Mathematics: Improper Fractions
  • For Everyday Use: Mixed Fractions


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