Question

How could Mrs. Mendoza divide the ream of paper equally between two art classes? She has a paper cutter to slice the paper, if needed. What will the dimensions for each sheet of paper be once she has divided the ream? How many sheets will each class recieve?

Answer 1

I need one detail to be sure: how many sheets are in the ream and what size are the sheets now? (Common U.S. values are 500 sheets per ream of letter paper, 8.5 in × 11 in.) Also tell me whether by “divide equally” you mean equal number of full sheets, or equal total paper area (so cutting is allowed).

Below are the usual interpretations with simple solutions. Replace the numbers if your ream or sheet size is different.

1) If the ream is 500 sheets of 8.5 in × 11 in and you want equal full sheets
- No cutting needed. Give each class 250 whole sheets.
- Dimensions of each sheet remain 8.5 in × 11 in.

2) If you want to cut every sheet in half so each class gets more smaller sheets
- Cut each sheet into two equal halves:
- Cutting across the 11 in side → halves are 8.5 in × 5.5 in.
- Cutting across the 8.5 in side → halves are 4.25 in × 11 in.
- Total pieces = 500 × 2 = 1000; each class gets 500 pieces of the chosen half-sheet size.

3) If you want quarter-sheets
- Cut each sheet into 4 equal pieces (cut both ways): pieces are 4.25 in × 5.5 in.
- Total pieces = 500 × 4 = 2000; each class gets 1000 pieces.

4) If the ream has an odd number of sheets (say 2k+1) and you want exactly equal paper area for each class
- Give each class k whole sheets and cut the remaining single sheet in half; give each class one half. Each class then has k + 0.5 sheet-equivalents (equal area). The half-sheet dimensions depend on which way you cut (as above).

If you tell me the exact ream size and which “equal” requirement you mean (equal full sheets vs equal area vs equal sheet sizes), I’ll give the precise final numbers and dimensions.