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:
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