A mixed fraction is part whole number, part fraction. For example: $5 \frac{3}{4}$.
It means, in effect: $5 + \frac{3}{4}$
## Converting mixed fractions into improper fractions
Mixed fractions are hard to calculate with. We need some way to convert them to fractions. We can do this by converting them to improper fractions.
With the example $4 \frac{7}{8}$, we know this means $4 + \frac{7}{8}$. We need to express the amount 4 in terms of eighths. It would be 4 lots of $\frac{8}{8}$ given that 4 is a whole number not a fractional amount. Thus the process would be:
But we know that when we [add fractions with a common denominator](./Add_Subtract_Fractions.md#adding-subracting-fractions-with-common-denominators), we only add the numerators, not the denominators. Thus the calculation would actually be:
$$
\frac{8 + 8 + 8 + 8 + 7}{8} = \frac{39}{8}
$$
Addition helps to explain the concepts underlying the procedure but it is more efficient to use multiplication.
The procedure is as follows:
1. Multiply the whole number part by the denominator
## Converting improper fractions into mixed fractions
It is quite obvious how to reverse the process and turn an improper fraction into a mixed fraction.
Take $\frac{27}{5}$. We work out how many times the numerator is divisible by the denominator and make that the whole number. The remainder is then left as the fractional part.
$$
\begin{split}
\frac{27}{5} = 27 \div 5 \\
= 5 r 2 \\
= 5 \frac{2}{5}
\end{split}
$$
## Multiplying and dividing by mixed fractions
Now that we know how to convert mixed fractions into improper fractions, it is straight forward to multiply and divide with them. We convert the mixed fraction into an improper fraction and then divide and multiply as we would with a proper fraction.
### Demonstration
Calculate $-2\frac{1}{12} \cdot 2 \frac{4}{5}$:
1. First convert each mixed fraction into an improper fraction:
