Recognise Mixed Numbers and Improper Fractions 6 - Reasoning

Zach has prepared a mathematical challenge that tests your understanding of improper fractions and their comparison to mixed numbers. The task is to identify all improper fractions that have 3 as their denominator and fall within the specific range of being greater than one third (1/3) but less than ten thirds (10/3). An improper fraction, unlike a mixed number, has a numerator that is larger than the denominator, resulting in a value greater than one whole.

Upon examining the range between 1/3 and 10/3, it's clear that there are several fractions that meet the criteria. The solution to Zach's quiz reveals that there are six improper fractions that satisfy the conditions: four thirds (4/3), five thirds (5/3), six thirds (6/3), seven thirds (7/3), eight thirds (8/3), and nine thirds (9/3). Each of these fractions has a numerator that is greater than 3, making them all improper, and they sequentially increase in value, fitting neatly within the specified range.