why do all the fragment sizes for each restriction enzyme add up to the same total?

Answer 1

Because they are all working on the same piece of material.

Consider if you have a chain that's CCCGGGTTTCCCGGG (15bases long)

Enzyme 1 cuts between C and G, so you get:
CCC and GGGTTTCCC and GGG

Enzyme 2 cuts between G and T, so you get:
CCCGGG and TTTCCCGGG

Both are still 15 bases when you add them up.

What if you're looking at the molecular weights? Let's say C=3, G =2, and T=1 of some weight. The entire chain would weigh 33 of that unit. Using enzyme 1 again, you would get 3 fragments that would weigh 9, 18 , and 3 (9+18+3 = 33). With enzyme 2, you'd get 2 fragments of 15+18 (15 + 18 = 33).

Consider this like taking a 12 inch piece of paper and cutting it. No matter where you make the cuts or how many you make, the lengths will still add up to 12 inches.

Hope this helps!

Answer 2

Um, I'm assuming you are asking why, when a piece of DNA is cut by various restriction enzymes, the total of all the fragments equals the same number of bases. If so, this is very simple. You are just cutting the strand at different sites, you are not eliminating DNA. When you add it all up it's as if you are putting the strand back together. Doesn't matter where you cut it.