Eddie Scheurer '27

Subtraction is seemingly a very simple concept within math—just the reversal of addition. Yet, usually in prealgebra, we are taught to think of the subtraction symbol as 

+(−1)+(−1)

That still isn’t the best representation of the abstract thought of the negative sign—it is in notation, recursive and hard to conceptually grasp. Rather, using the addition of 1D vectors is a better mental representation of subtraction because it allows for connection to older concepts and also for higher thought by means of subtraction. 

What does 1D vector mean? Essentially, it’s an arrow on a number line equal in length to the number you want, so 

5−35−3

can be represented through two opposite-direction arrows of length 5 towards positive infinity, and length 3 towards negative infinity; after equalizing the opposing forces, you end with a force of two towards positive infinity. 

You can extend this way of thought to do something like this: 

−5734+45−44+53+92−723−19−27+357−5734+45−44+53+92−723−19−27+357

Despite its size, this can be worked through by adding together each sign separately; start by sorting each number by sign, and then size. 

45+53+92+357−5734−44−723−19−2745+53+92+357−5734−44−723−19−27

357+92+53+45−5734−723−44−27−19357+92+53+45−5734−723−44−27−19

Approaching the above problem is now far easier: 547 towards positive infinity, and 6547 towards negative infinity. The ending force is 6000 towards negative infinity. 

Subtraction is just vectors.M