When we're doing arithmetic (addition, subtraction, multiplication, division), we have a number and an operator and another number. Does it matter which number comes first?
Question
Does 3 + 2 = 2 + 3?
Does 3 - 2 = 2 - 3?
Does 3 x 2 = 2 x 3?
Does 3 ÷ 2 = 2 ÷ 3?
Which operations are Commutative?Answer
Of the four arithmetic operations, only Addition and Multiplication are Commutative.Analysis
We're talking about the importance of knowing which term goes first. Does it really matter? It's the Commutative Property that helps to tell us.
For an operation to be Commutative, it needs to satisfy the relation A operator B = B operator A.
We can work examples to show which operations are Commutative and which aren't.
To help with my examples, I'm going to say that A = 3 and B = 2.
Addition
For addition to be commutative, A + B has to be equal to B + A. Is it?
3 + 2 = 2 + 3
5 = 5 ✅
And we can see this on a number line (3 + 2 is blue and 2 + 3 is purple):
Addition is commutative.
Subtraction
For subtraction to be commutative, A - B has to be equal to B - A. Is it?
3 - 2 = 2 - 3
1 = -1 No.
And we can see this on a number line (3 - 2 is blue and 2 - 3 is purple):
Subtraction is not commutative.
Multiplication
For multiplication to be commutative, A X B has to be equal to B X A. Is it?
3 x 2 = 2 x 3
6 = 6 ✅
And we can see this using cubes.
This is 3 x 2:
This is 2 x 3:
Multiplication is commutative.
Division
For division to be commutative, A ÷ B has to be equal to B ÷ A. Is it?
3 ÷ 2 = 2 ÷ 3
No.We can do this with blocks with
above and 
below (the result of the division is one section of each of the set of blocks):
Division is not commutative.
For more information check out these links (comment to add your favourite link):
Where might you have come from?
Fact-orials Index
Numbers:
Operations:
Where might we go?
Operations with different kinds of numbers:
Properties:
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