What is the name of the property that reducing a value by $a\%$, then by $b\%$, is the same as reducing by $b\%$, then by $a\%$?

Question

Suppose we have a number $x$.

I reduce $x$ by $a$% and then by $b$%.

This is the same as reducing $x$ by $b$% and then by $a$%.

What would I call this? Is it okay to describe this as percentages being "associative"?

Is there an intuitive explanation for why this is true? It's of course simple to prove algebraically, but it's not intuitive to me at least.

Answer 1

It is the commutative property. Reducing $x$ by $a\%$ is the same as doing $x\cdot(1-\frac{a}{100})$, and similarly reducing $x$ by $b\%$ is the same as doing $x\cdot(1-\frac{b}{100})$.

Reducing $x$ by both $a\%$ and $b\%$ is the same as multiplying $x$ by both of those factors, and the commutative property of multiplication allows it to be done in either order.