Question

Can we multiply numbers in any order obtaining the same result?

Answer 1

Yes, their order doesn’t matter you always get the same result.

Explanation:

This is called the commutative property of multiplication. If `a,b` are numbers, then `a xx b = bxxa`.

Answer 2

Yes, since multiplication is both commutative and associative.

Explanation:

If `a` and `b` are any two (ordinary) numbers then:

`a xx b = b xx a`

This is called the commutative property of multiplication.

If `a`, `b` and `c` are any three (ordinary) numbers then:

`a xx (b xx c) = (a xx b) xx c`

This is called the associative property of multiplication.

As a result of the associative property, we can write:

`a xx b xx c`

unambiguously without any parentheses.

Combining these two properties, we can multiply numbers in any order and always get the same result.

Advanced footnote

Note that above I said ordinary numbers. There are some strange kinds of numbers that do not conform to these rules:

• Hamilton's quaternions drop the requirement that multiplication be commutative.

• Octonions drop the requirement that multiplication be associative.

See https://socratic.org/questions/are-octonions-numbers for some more details.