Yes - integers are called so no matter whether they are positive or negative.
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No, not every negative number is an integer. For example, -11/2 is not an integer. However, -1, -2, -3, and so on, are negative integers. Perhaps that is what you meant to ask. The negative of every positive integer is a negative integer.
Yes the integer group includes negative numbers, positive numbers, and 0.
Yes. ie) -8-3=x The problem would change to: -8+(-3)=x x=-11 So just make it a negative plus a negative.
10 - 21 = -11
A negative integer multiplied by a negative integer is always a positive integer product. -x * -y = xy