*Before learning about mixed fractions, please make sure you've read the primer on fractions. *

**Mixed fractions** consist of a
whole number and a fraction. They are otherwise known as **mixed numbers**.

Examples include

**1 3/4 2 1/2 4 2/3 7 1/6**

Converting improper fractions to mixed numbers has been considered here.

To convert a mixed number to an improper fraction, we first need to convert the whole number into a fraction.

For instance, take

**1 3/4**

which can also be expressed

**1 + 3/4**

The denominator of the fraction into which the whole number 1 is going to be converted will be the same as the denominator in the fraction 3/4 - i.e. 4.

The numerator of the fraction into which the whole number 1 is going to be converted equals the denominator multiplied by the whole number – i.e. 4 x 1 = 4.

So we can write the whole number 1 as the fraction 4/4.

1 + 3/4 becomes

**4/4 + 3/4**

Adding these fractions together gives

**7/4**

i.e. the mixed number 1 3/4 is equal to the improper fraction 7/4.

Moving onto 2 1/2

Or

**2 + 1/2**

First convert the whole number 2 into a fraction.

The denominator will be 2 (the same as the denominator in the fraction 1/2).

The numerator equals the denominator times by the whole number – i.e. 2 x 2 = 4.

So the whole number 2 is equal to the fraction 4/2.

Now we can write

**2 + 1/2 = 4/2 + 1/2**

and

**4/2 + 1/2 = 5/2**

Therefore 2 1/2 is the same as 5/2.

What about 4 2/3 (or 4 + 2/3)?

The denominator of the fraction 2/3 is 3 - this also becomes the denominator of the fraction into which the whole number is converted.

The whole number 4 can be written as 12/3 (because the product of multiplying the denominator by the whole number = 3 x 4 = 12).

So

4 2/3 = 12/3 + 2/3

4 2/3 = 14/3

One more case of mixed fractions!

** **

7 1/6 = 7 + 1/6

Taking the denominator 6 of the fraction 1/6, the whole number 7 can be written as 42/6 (denominator x whole number = 6 x 7 = 42).

Therefore

7 1/6 = 42/6 + 1/6

7 1/6 = 43/6

To recap

The terms **mixed fraction** and **mixed number** are interchangeable.

Mixed number = whole number + fraction.

**When converting mixed numbers to improper fractions:**

** **

the denominator of the existing fraction also becomes the denominator of the fraction into which the whole number is converted;

multiplying the denominator by the whole number gives the numerator of the fraction into which the whole number is converted;

adding together the resulting fraction and the existing fraction gives the improper fraction equivalent of the mixed number.

For more on fractions click: