name- danielle level of question: elementary/middle who is asking question: preservice teacher

I am embarrased to be asking this question, but... is it possible to have a fraction with a zero? For example, 0/4. This does not make sense to me and I do not know what it would be representing, other than nothing! Is it proper to express such a fraction?

Thanks!

The fraction  ⁰/₄ does represent something. What it represents is zero.

Suppose that I have 12 pencils to distribute to 4 students so that each student gets the same number of pencils. How many pencils do I give to each student? This is the classic division problem. The number of pencils I give to each student is  ¹²/₄ = 3.

Now suppose that I have 0 pencils. If I distribute these pencils among the 4 student then each student gets  ⁰/₄ = 0 pencils.

Maybe it helps to consider an example where the measurement is length.

• If I cut a 12 inch piece of licorice into 4 equal pieces then each piece is  ¹²/₄ = 3 inches long.
  
  
• If I cut a 4 inch piece of licorice into 4 equal pieces then each piece is  ⁴/₄ = 1 inch long.
  
  
• If I cut a  ¹/₂ inch piece of licorice into 4 equal pieces then each piece is  (¹/₂)/₄ = ¹/₈ inches long.
  
  
• If I cut a 0 inch piece of licorice into 4 equal pieces then each piece is  ⁰/₄ = 0 inchs long.