The following uses the universal constant H = -1. This represents a half turn along a circle, like I represents a quarter turn. Observe that a - (-b) = a + H H b, so that this particular subtraction actually involves multiplication, which indicates why pupils find this hard. Also 5/2 can be written as 2 + 2^H, so that it is clearer where it is on the number line. Pierre van Hiele (1909-2010) already proposed to get rid of the fractional form y / x, and instead use y x^-1. The latter may be confusing for pupils since they might think that they must subtract something. However, the use of an algebraic symbol clinches the proposal. The choice of H is well-considered: its shape reminds of -1. Pronounce H as Eta or "symbolic -1". This notebook provides a package to support the use of H in Mathematica. See the attachment or:

https://www.wolframcloud.com/objects/thomas-cool/MathEd/2018-04-02-Arithmetic-with-H.nb

Attachments:

2018-04-02-Arith...nb