Mixed fractions (mixed numbers)


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


How to convert mixed numbers to improper fractions


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:

Math fractions

Equivalent fractions

Simplifying fractions

Adding fractions

How to subtract fractions

Multiplying fractions

How to divide fractions

Improper fractions

Comparing fractions

Ordering fractions

Fraction to decimal

Fraction to decimal chart

Decimal to fraction

Fraction to percent

Percent to fraction


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