Why does adding a positive and negative integer always result in a negative integer?

Answer 1

It won't always result in a negative integer. Multiplyinga positive number and a negative number always results in a negative number. For example 3 x -2 = -6. Adding a positive number and a negative number can result in a negative number but it does not have to.

When adding a positive number with a negative number, we really subtract from the largest number in the absolute value the smallest number in the absolute value, and we keep the sign of the number with the larger absolute value. So the sign of the number with the larger absolute value will determine the sign of the answer.

Some examples:

10 + (-7) = 3

Here, 10 is the largest number in the absolute value, because |10| = 10, and |-7| = 7. So, 10-7=3. 3 will be positive since 10 was positive

7 + (-10) = -3

Here, -10 is the largest number in absolute value, because |-10| = 10, and |7| = 7. So, 10 - 7 = 3. 3 will be a negative number since -10 was negative number. Thus, the answer will be -3.

-10 + 7 = -3

-7 + 10 = 3

It all depends on whether the number with the larger absolute value is negative or positive. If it is positive then the answer will be positive. If it is negative then the answer will be negative. If the two numbers have an equal absolute value, then the result is zero, which is neither positive nor negative.