Mixed Fractions

(Also called "Mixed Numbers")

4/43/4
3
4
(one and three-quarters)
A Mixed Fraction is a whole number and a proper fraction combined.

such as 1 3/4 .

Examples

2 3/8 7 1/4 1 14/15 21 4/5

See how each example is made up of a whole number and a proper fraction together? That is why it is called a "mixed" fraction (or mixed number).

Names

We can give names to every part of a mixed fraction:

Three Types of Fractions

There are three types of fraction:

Fraction Types

Mixed Fractions or Improper Fractions

You 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
=

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
  • Write that 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:

17
5

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
4

When to Use Improper Fractions or Mixed Fractions

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"

But for mathematics improper fractions 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

 

We Recommend:

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