Question

An eighth-grade student claims she can prove that subtraction of integers is commutative. She points out that if a and b are integers, then a – b = a + -b. Since addition is commutative, so is subtraction. What is your response?

Answer 1

Subtraction is not commutative. We can see this with a counterexample.

Let a = 2 and b = 3


So a - b = 2-3 = -1


but...


b - a = 3-2 = 1


So because -1 does not equal 1, this tells us that a - b does not equal b - a


So subtraction is not commutative.

Answer 2

thank you

Answer 3

np