When adding a positive to a negative, the first step is to change the sign of the negative integer to a positive.
Example: 9 + (-4) becomes 9 + 4. The second step is to change the equation from addition to subtraction. In this case you now have: 9 - 4. Finally, solve the equation but keep the sign of the larger number from the original equation.
Example: 9 + (-4) = x. Subtract 9 -4 = x. Take the sign of 9, which is the larger number, from the original equation. The final answer is positive 5.
Example: 4 + (-9) = x. Subtract 4 - 9 = x. In this case take the sign of - 9 which is the the larger number from the original equation. The final answer is negative 5.
When adding two numbers with equal absolute values, but one is positive and one is negative, your sum will always be zero.
Example: 40 + (-40) = x. Subtract 40 - 40 = x, Solve to 40 - 40 = 0.
By following the addition rule, each number will cancel the other to result in zero. This scenario, where two integers are added and solve to zero, is known as the additive inverse.
This is the most simple rule for adding negative integers. In this case, you add the two integers and keep the sign. As a result, when adding negative integers you will always have a negative integer as the sum. This is because you are moving left of zero, or in a negative direction on the number line, when you add negative integers.
Example. -7 + (-3) = -10.
Adding integers is quite simple and the rules are fairly straightforward. Just remember that two negative integers will always result in a negative, and that the sign of the larger integer determines the sign of the sum when the integers are of different signs. If you are having trouble with these concepts draw a number line for practice. Place a zero in the middle of your line and place the numbers 1 through 10 on the right of zero and -1 through -10, beginning with -1 closest to the zero and to the left of it. This will help you visualize the relationship and understand the concepts of adding negative integers.