# Addition and Subtraction of Integers

The addition rules for integers state that when two integers are combined, the result is the sum of the two integers. The rules also state that when a negative integer is combined with a positive integer, the result is a negative integer. When two negative integers are combined, the result is a negative integer.

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## Rules for Addition and Subtraction of Integers

• To add two or more integers, add the absolute values of the integers and keep track of the sign.
• For example, to add the integers -5 and 7, first add the absolute values: 5 + 7 = 12. Then, keep track of the sign. Because the sum is positive, the sign is positive. Therefore, the final answer is +12.
• To add three or more integers, add the absolute values of the integers and keep track of the sign.
• For example, to add the integers -5, 7, and 9, first add the absolute values: 5 + 7 + 9 = 21. Then, keep track of the sign. Because the sum is positive, the sign is positive. Therefore, the final answer is +21.
• If one of the integers is negative, the sign of the sum is negative.
• For example, to add the integers -5 and -7, first add the absolute values: 5 + (-7) = -2. Then, keep track of the sign. Because the sum is negative, the sign is negative. Therefore, the final answer is -2.

### Subtraction of Integers

• To subtract two or more integers, subtract the absolute values of the integers and keep track of the sign.
• For example, to subtract the integers 7 and 5, first subtract the absolute values: 5 – 7 = -2. Then

## Positive and Negative Rules

There are a number of different ways to think about positive and negative rules, but one way to think of them is as follows:

• A positive rule is a rule that leads to desirable outcomes, while a negative rule is a rule that leads to undesirable outcomes.
• Another way to think about it is that a positive rule is a rule that promotes happiness and well-being, while a negative rule is a rule that promotes unhappiness and suffering.
• Positive and negative rules can also be thought of in terms of freedom and coercion. A positive rule is a rule that allows people to lead happy and fulfilling lives, while a negative rule is a rule that restricts people’s freedom and causes them to suffer.

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2 + 3 = 5

-4 + 5 = 1

6 + (-8) = -2

## Subtraction of Integers

To subtract two integers, use the following steps:

Line the integers up vertically so that the ones digits are lined up.

For the number on the right, subtract the number on the left. Write the answer below the number on the right.

If the number on the right is less than zero, write the number below the line in parentheses.

Here is an example:

-5

-2

-7

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