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Which operations are commutative and

associative?
addition
O subtraction
multiplication
division

User Tsunamis
by
7.9k points

2 Answers

4 votes

Answer:

addition

multiplication

User Erik Henriksson
by
8.6k points
5 votes

Answer:

  • addition
  • multiplication

Explanation:

When learning about commutative and associative properties, we learn that ...

a + b = b + a . . . . . addition is commutative

ab = ba . . . . . . . . . multiplication is commutative

But we also know that ...

a - b ≠ b - a . . . . . . subtraction is not commutative

a/b ≠ b/a . . . . . . . . division is not commutative

__

We also learn that ...

a + (b+c) = (a+b) +c . . . . addition is associative

a(bc) = (ab)c . . . . . multiplication is associative

And of course, ...

a - (b -c) ≠ (a -b) -c . . . . subtraction is not associative

a/(b/c) ≠ (a/b)/c . . . . . . . division is not associative

_____

However, you can use associative and commutative properties in problems involving subtraction and division if you write the expression properly:

a - (b - c) = a +(-(b -c)) = a +((-b) +c) = (a +(-b)) +c . . . . keeping the sign with the value makes it an addition problem, so the associative property can apply

(a/b)/c = (a(1/b))(1/c) = a(1/b·1/c) = writing the division as multiplication by a reciprocal makes it so the associative property can apply

User Peter Jack
by
7.4k points

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