How I evaluate 5+(-11)-(-11)

  5

Step-by-step explanation:

First of all, look at what you have.

The problem is in the form ...

  5 + x - x

where x = -11

You know that (x - x) = 0, so this is equivalent to ...

  5 + 0 = 5

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If you go by the order of operations, you first eliminate parentheses. For +(-11), this means that you can write it as -11:

  5 -11 -(-11)

For -(-11), the minus sign outside parentheses means you need to change the sign inside parentheses to get  +11:

  5 -11 +11

Continuing with the order of operations, you combine the first two terms:

  -6 +11

Then the last two:

  5

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The deal with addition is that it is commutative and associative. That is, you can rearrange the terms of a sum to any convenient order, and the result will be the same. (Be sure to keep the sign with the number.)

In this case, once we get the signs sorted out, the sum can be written as ...

  11 -11 +5 = 0 +5 = 5

so it is easy to see that the 11s cancel each other.

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