The fold-and-rip method works or doesn't work based on the type of paper you are working with. Paper that is made on rolls (most office paper, newsprint, paper towel, etc) has a 'grain'. The pulp fibers all align in a certain direction (typically with office paper, the long direction).
It's quite easy to fold-and-tear this type of paper along this axis. It's rather difficult along the other axis.
Some ways to make this easier:
- Do a double fold (fold one way, then the other, to try and break the fibers along the fold)
- Once folded, find a solid straight edge to lay on one side of the fold, and then tear the other side in an upward motion along the straight edge
- Prior to tearing, moisten the fold to help loosen the fibers.
At the end of the day, though, you'll still find that you can't do this successfully 100% of the time. The paper's grain just makes that difficult.
The other way to make paper is via matts/screens. In this scenario, there is no grain as the pulp fibers align themselves all in random directions. Paper made on matts tends to be artist's papers such as watercolor paper, thick cotton rag, printmaking paper, etc.
These papers are actually incredibly easy to tear along a straight line with just a straight edge. No need for fold at all.
Other ways to cut paper if you have a good straight edge to use:
- run a knife along the straight edge
- run a 'roller cutter' along the straight edge (typically used to cut fabric)
- open up your scissors and use one side as a knife blade along the straight edge.