1. What is a proper fraction?
A proper fraction is one where the numerator (the top line) is SMALLER than the denominator (the bottom line).
An improper fraction has a numerator which is BIGGER than the denominator.
2. Should a number be shown as an improper fraction or as a mixed number?
Sometimes it is easier to use fractions shown as mixed numbers and sometimes as improper fractions.
e.g. When adding and subtracting fractions you can use mixed numbers and then add or subtract the whole number parts and then the fractions.
When multiplying or dividing it is best to use the fraction as improper fraction.