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Improper Fractions

Quick Definition: An Improper fraction has a
numerator (top number) larger than or equal to
the denominator (bottom number),

such as 7/4 or 4/3

(It is "top-heavy")

(seven-fourths or seven-quarters)


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

We call the top number the Numerator, it is the number of parts you have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.

Fractions can have three different types :

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 Fractions

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


3/2 7/4 16/15

Improper Fractions = 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


Are Improper Fractions Bad ?

NO, they aren't bad ! For mathematics they are actually better than mixed fractions. Mixed fractions can be confusing when you write them down in a formula:

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  

But, for everyday use, people understand mixed fractions better. It is easier to say "I ate 2 1/4 sausages", than "I ate 9/4 sausages"

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 that is a type of improper fraction.

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.

Divide: 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: