- #1

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- 3

## Summary:

- Commutative & Associative property of addition of negative numbers.

Commutative property of addition.

If a & b are integers then,

a+b = b+a

2+3 = 3+2

5.

Does not work for subtraction.

2-3 = -1

3-2= 1

Having said that, what about the special case with negative numbers

-5 + 7 = 2 & 7 + (-5) = 2.

15 -7 = 8 & -7 + 15 = 7.

Associative property of addition.

If a, b & c are integers then,

a + (b+c) = (a+b) + c

2 + (3+4) = (2+3) + 4

2+7 = 5+4

9.

I tried 5 scenarios for the above,

a= - b = + c= -

a= + b= - c=+

a=+ b=+ c=-

a=- b=- c=+

a=- b=- c=-

And they all seem to work. It also seems to work for negative numbers in multiplication as well.

Is there a special case for commutativity & associativity for negative numbers?

If a & b are integers then,

a+b = b+a

2+3 = 3+2

5.

Does not work for subtraction.

2-3 = -1

3-2= 1

Having said that, what about the special case with negative numbers

**(when we also move their respective signs)**-5 + 7 = 2 & 7 + (-5) = 2.

15 -7 = 8 & -7 + 15 = 7.

Associative property of addition.

If a, b & c are integers then,

a + (b+c) = (a+b) + c

2 + (3+4) = (2+3) + 4

2+7 = 5+4

9.

I tried 5 scenarios for the above,

a= - b = + c= -

a= + b= - c=+

a=+ b=+ c=-

a=- b=- c=+

a=- b=- c=-

And they all seem to work. It also seems to work for negative numbers in multiplication as well.

Is there a special case for commutativity & associativity for negative numbers?