Number System: Mixed Fractions

Mixed Fractions

(Also called "Mixed Numbers")

		A Mixed Fraction is a whole number and a proper fraction combined. such as 1 3/4.
1 3/4
(one and three-quarters)

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:

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 multipled?):

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

We Recommend:

For Mathematics: Improper Fractions
For Everyday Use: Mixed Fractions

Posted in: Fractions, Mixed Fractions