Is there a commutative property of addition, subtraction, multiplication, or division and does order matter when doing any of them, why or why not?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

An operation between two numbers x and y is commutative if changing the order of x and y does not alter the result.

  • For addition, the commutative property holds as x + y = y + x. For example 3 + 6 = 9 and 6 + 3 = 9.
  • For multiplication also the commutative property holds as x*y = y*x. For example 6*3 = 18 and 3*6 = 18
  • The commutative property does not hold for subtraction and division.

This follows from the fact that x - y is not the equal to y - x. For example 6 - 3 = 3 but 3 - 6 = -3

Also, for x and y, x/y does not give the same result as y/x. For example 6/3 = 2 but 3/6 = 1/2.

sultlete's profile pic

sultlete | Student | (Level 1) Honors

Posted on

Addition and Multiplication ARE commutative, while Subtraction and Division are NOT commutative.

e.g, in simple addition and multiplication, no matter what the order, the result is still the same. Whereas, subraction and division need to have a particular order or the result will change.

When doing more complex expressions and equations, order IS important or the answer will change completely.

An easy way to remember order is BIMDAS

B - Brackets
I - Indices
M - Multiplication (from left of expression to right)
D - Division (from left of expression to right)
A - Addition(Left of expression to right)
S- Subtraction (Left of expression to right)

Hope that helped.

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