1) Identify the type
For each item, decide whether it is:
- Proper fraction: the numerator is smaller than the denominator.
- Improper fraction: the numerator is greater than or equal to the denominator.
- Mixed number: a whole number together with a fraction.
2) Compare the parts
For fractions, compare the top number and the bottom number directly:
- If the top number is less than the bottom number, it is proper.
- If the top number is at least the bottom number, it is improper.
For mixed numbers, look for a whole number written beside a fraction, such as 2 1/3.
3) Use the definition as a check
A proper fraction represents less than 1 whole, while an improper fraction represents 1 whole or more. A mixed number also represents 1 whole or more, but it is written in a different form.
4) Quick checking method
If you are unsure, ask:
- Is there a whole number written with the fraction? Then it is mixed.
- If not, is the numerator smaller than the denominator? Then it is proper.
- Otherwise, it is improper.
5) Final check
Make sure your answer matches the form of the expression. A correct classification should agree with both the numbers and the way the number is written.