The following are rules to follow when adding and subtracting integers.

1. Adding integers with the same sign – The sign of the sum (answer) is the same as the sign of the two addends (values being added). If you add 2 positive integers, the sum will be positive. If you add two negative integers, the sum will be negative. To find the value, you simply add the 2 values.

Ex. : 5 + 2 will have a positive answer, because 5 and 2 are positive. Then, you add the values of 5 and 2 to get 7. (-2) + (-5) will have a negative answer, because both are negative. The value of 5 and 2 are still 7, but the answer will be (-7).

Adding Integers with different signs – When the addends have different signs (one is positive, one negative), the sign of the sum (answer) is the same as the addend that is farther from zero (has the largest absolute value). Once you get the sign, you can subtract the values. See examples below:

Ex. 1 + (-5) –> (-5) is farther from zero (has a high absolute value), so the sum will be negative. Then you have 5 – 1 = 4, so your answer is (-4), because we knew the answer will have a negative value. (-15) + 35 –> 35 is farther from zero, so we know our answer will be positive. Then, 35 -15 = 20. Because our answer is positive, it stays as 20.

Subtracting Integers

You do not **need** to subtract integers. Why? Subtracting an integer is the same thing as adding its opposite.

Subtracting a positive integer is the same as adding the negative integer. 2 – 4 = 2 + (-4) –> Both equal (-2).

Subtracting a negative integer is the same thing as adding the positive integer. 2 – (-4) = 2 + 4 –> Both equal 6.

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