Say you're adding -2+(-2). Adding negative two is equavilant to subtracting positive two. Both -2+(-2) would be -4. I hope that made sense.
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the sum of two negative integers is ALWAYS negative
Yes, the sum of two negative integers is always negative.
for integers with tow different signs, it will always be negative in multiplying and division. for adding and subtracting, the sign is for the bigger number.
No the product of two integers will not always be a positive, because if you multiply a positive and a negative you'll get a negative.
Yes