# Mixed Fractions

(Also called "Mixed Numbers")

 1 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:

## 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 (3) by the fraction's denominator (5):

3 × 5 = 15

Add the fraction's numerator (2) to that:

15 + 2 = 17

Then put that 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 in a formula: should the two parts be added or multiplied?

 Mixed Fraction: Improper 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 ? What is: 1 + 9/4 ? It is: 4/4 + 9/4 = 13/4

We Recommend:

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