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Mixed and improper fractions
Improper fractions
- Proper fraction:
- The numerator is smaller than the denominator
- E.g.
\frac{2}{3},-\frac{5}{10}
- Improper fraction
- The numerator is greater than the denominator
- E.g.
\frac{3}{2},-\frac{5}{4}
Mixed fractions
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:
\frac{8}{8} + \frac{8}{8} + \frac{8}{8} + \frac{8}{8} + \frac{7}{8}
But we know that when we add fractions with a common denominator, 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:
- Multiply the whole number part by the denominator
- Add the numerator
- Place the result over the denominator
Thus:
4 \frac{7}{8} = \frac{(4 \cdot 8) + 7 }{8}