Which operations are commutative and
associative?
addition
o subtraction
multiplication
division

Step-by-step 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

on friday there were 15 birds

lol.

it's ok we all do this sometimes.

-aparri