Mixed Numbers | Elementary

A mixed number, or mixed fraction, consists of a whole number and a fraction part.

In the mixed number |6\ \dfrac{1}{4}|, the whole number is |6| and the fraction is |\dfrac{1}{4}|.
We represent the number with |6| wholes and |1| quarter..

The mixed number |6\ \dfrac{1}{4}| is equivalent to the fraction |\dfrac{25}{4}|.

When you read a mixed number, you have to add an "and" between the whole number and the fraction.
 |6\ \dfrac{1}{4}| therefore reads as "six and one quarter".

1. I divide the numerator by the denominator. Then I write down the quotient (the answer) and the remainder.
    
2. I write the quotient as the whole part of the mixed number and the remainder as the fraction’s numerator.
    
3. I write down the denominator of the initial fraction for the denominator of the fraction of the new mixed number. 

What is |\dfrac{39}{7}| as a mixed number?

The fraction |\dfrac{39}{7}| is equivalent to the mixed number |5\ \dfrac{4}{7}|.

1. I convert the whole number part into a fraction by putting it over |1|.
    
2. I multiply the denominator of the new fraction by the denominator of the fraction in the mixed number.
    
3. I multiply the numerator of the new fraction by the same number.
    
4. I add the fraction obtained to the fraction part of the mixed number. 

Write the mixed number |5\ \dfrac{4}{7}| as a fraction.

I convert the whole number part into a fraction by putting it over |1|.
I multiply the denominator of the new fraction by the denominator of the fraction in the mixed number.  The denominator of the fraction |\dfrac{4}{7}| is |7|.
I multiply the numerator of the new fraction by the same number.
I add the fraction you obtain to the fraction part of the mixed number.  To learn how to add fractions, I can read this concept sheet: Addition of Fractions.

The mixed number |5\ \dfrac{4}{7}| is equivalent to the fraction |\dfrac{39}{7}|.