Can we multiply numbers in any order obtaining the same result?
2 Answers
Yes, their order doesn’t matter you always get the same result.
Explanation:
This is called the commutative property of multiplication. If
Yes, since multiplication is both commutative and associative.
Explanation:
If
#a xx b = b xx a#
This is called the commutative property of multiplication.
If
#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.
