How to turn a improper fraction into a proper fraction

Calculator Use

Convert improper fractions to mixed numbers in simplest form. This calculator also simplifies proper fractions by reducing to lowest terms and showing the work involved.

In order to simplify a fraction there must be:

  1. A number that will divide evenly into both the numerator and denominator so it can be reduced, or
  2. The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number.

What is an Improper Fraction?

An improper fraction is any fraction where the numerator is greater than the denominator. Examples of improper fractions are 16/3, 81/9, 525/71.

How to Convert an Improper Fraction to a Mixed Number

  1. Divide the numerator by the denominator
  2. Write down the whole number result
  3. Use the remainder as the new numerator over the denominator. This is the fraction part of the mixed number.

Example: Convert the improper fraction 16/3 to a mixed number.

  1. Divide 16 by 3: 16 ÷ 3 = 5 with remainder of 1
  2. The whole number result is 5
  3. The remainder is 1. With 1 as the numerator and 3 as the denominator, the fraction part of the mixed number is 1/3.
  4. The mixed number is 5 1/3. So 16/3 = 5 1/3.

When possible this calculator first reduces an improper fraction to lowest terms before finding the mixed number form.

Example: Convert the improper fraction 45/10 to a mixed number.

  • This calculator reduces the improper fraction to lowest terms by dividing numerator and denominator by the greatest common factor (GCF). The GCF of 45 and 10 is 5.
  • \( \dfrac{45\div5}{10\div5} = \dfrac{9}{2}\)

  • Use this reduced improper fraction and divide 9 by 2: 9 ÷ 2 = 4 with remainder of 1
  • The whole number result is 4
  • The remainder is 1. With 1 as the numerator and 2 as the reduced denominator, the fraction part of the mixed number is 1/2.
  • The mixed number 4 1/2. So 45/10 = 4 1/2.

For additional explanation of factoring numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator.

If your improper fraction numbers are large you can use the Long Division with Remainders Calculator to find whole number and remainder values when simplifying fractions by hand.

To perform math operations on fractions before you simplify them try our Fractions Calculator. This calculator will also simplify improper fractions into mixed numbers.

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

It is usually "top-heavy"

More Examples

32 73 1615 1515 1005

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:

Fractions

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

NumeratorDenominator

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

Improper Fraction

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.

How to turn a improper fraction into a proper fraction

44

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.

Improper Fractions or Mixed Fractions

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

For example 134 = 74, as shown here:

Converting Improper Fractions to Mixed Fractions

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

How to turn a improper fraction into a proper fraction
  • Divide the numerator by the denominator.
  • Write down the whole number answer
  • Then write down any remainder above the denominator.
   

Example: Convert 114 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).

Answer:

2 34

That example can be written like this:

Example: Convert 103 to a mixed fraction.

Answer:

3 13

Converting Mixed Fractions to Improper Fractions

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

How to turn a improper fraction into a proper fraction
  • 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 325 to an improper fraction.

Multiply the whole number part by the denominator:

3 × 5 = 15

Add that to the numerator:

15 + 2 = 17

Then write that result above the denominator:

175

We can do the numerator in one go:

Example: Convert 219 to an improper fraction.

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 we write them in a formula: should the two parts be added or multiplied?

Mixed Fraction:   What is:   1 + 214   ?    
    Is it:   1 + 2 + 14   = 314 ?
    Or is it:   1 + 2 × 14   = 112 ?
             
Improper Fraction:  What is:   1 + 94   ?    
    It is:   44 + 94 = 134  

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

Example: It is easier to say "I ate 214 sausages", than "I ate 94 sausages"


We Recommend:

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

How do you make an improper fraction into a proper fraction?

Multiply the denominator of the fraction by the whole number. Add this result to the numerator of the fraction. This answer becomes the numerator of the improper fraction. Notice that the denominator of the improper fraction is the same as the denominator that was in the fractional part of the mixed number.