Associativity in arithmetic means that the order of operations does not matter. As a simple example, addition is associative: adding combines amounts and therefore the order of combining does not matter.

By contrast, subtracting is not associative – the order does matter. Remove 12p from 20p from 90p, could mean: remove 12p from 20p (giving 8p) and remove that from 90p to give 82p. Alternatively, it could mean remove 12p and 20p from 90p (giving 58p).

The basic formula for this does not help: 90 – 20 – 12.

You have to remember your arithmetic rules (often called BODMAS) to get it right. If you don’t remember, then you might use 90 – 20 – 12 incorrectly.

Associativity in Mathematics and Arithmetic Operators

 

EQUS helps to clarify what’s going on by automatically showing the order of operations, as in the above image.

This is just a simple example. Other operations, such as divide, are also not associative. And when different operators are combined with other operators, understanding what a formula is actually doing can become very difficult without visualizing it manually or using an EQUS visualization.