Short Answer 
The process of dividing a cupcake into thirds shows that one-third of it is claimed by you and your sister, while your cousin claims ten-thirds, which equals more than three cupcakes. This improper fraction of 10/3 is converted to a mixed number, resulting in 3 and 1/3, indicating that your cousin has over three full cupcakes.
Step 1: Understand the Division of the Cupcake
When dividing a cupcake into third parts, you’re splitting it into three equal sections. Each section represents one-third (1/3) of the cupcake. You receive one-third, your sister gets another third, and your cousin claims ten-thirds, indicating a total that exceeds one whole cupcake.
Step 2: Analyze Your Cousin’s Share
Your cousin’s claim of 10/3 or ten-thirds reflects a quantity greater than a single cupcake. To comprehend this share, consider it as whole cupcakes. Since three-thirds make one whole cupcake, your cousin has:
- Three full cupcakes from the first 9 thirds
- Plus an extra one-third from the remaining third
Step 3: Convert the Fraction to a Mixed Number
An improper fraction occurs when the numerator (10) is greater than the denominator (3). To convert it into a mixed number, divide 10 by 3 which results in:
- A whole number part: 3
- A remainder serving as the new fraction’s numerator: 1
Thus, 10/3 converts to 3 and 1/3, illustrating that your cousin possesses more than three cupcakes in total.