Integer Rules

Knowing your integer rules is crucial in Algebra!

You must know these rules as well as you know your addition facts! And... I'm hoping you know those facts by heart!

So... I'm going to give you a quick overview of the rules below and then if you want more step by step instruction, click the links provided!

If you are just beginning your study of integers, start with our basic integers lesson.

Adding Integers

There are two rules for adding integers and the rule that is used depends on the sign of the numbers that you are adding.

Adding Numbers with the Same Sign

If the numbers that you are adding have the same sign, then add the numbers and keep the sign.


-5 + (-6) = -11

Adding Numbers with Different Signs

If the numbers that you are adding have different (opposite) signs, then SUBTRACT the numbers and take the sign of the number with the largest absolute value.


-6 + 5= -1

12 + (-4) = 8

For more information on adding integers, visit our adding integers lesson.

Subtracting Integers

When subtracting integers, I use one main rule and that is to rewrite the subtracting problem as an addition problem. Then use the addition rules.

When you subtract, you are really adding the opposite, so I use theKeep-Change-Change rule.

The Keep-Change-Change rule means:

Keep the first number the same.

Change the minus sign to a plus sign.

Change the sign of the second number to its opposite.


12 - (-5) =

12 + 5 = 17

For more examples on subtracting integers, please visit our subtracting integers lesson.

Multiplying and Dividing Integers

The great thing about multiplying and dividing integers is that there is two rules and they apply to both multiplication and division!

Again, you must analyze the signs of the numbers that you are multiplying or dividing.

The rules are:

  • If the signs are the same, then the answer is positive.

  • If the signs are different, then then answer is negative.

Yes, that's definitely the easiest set of rules to remember for integers. If you need more clarification, then visit our page on multiplying and dividing integers.

That's it for integer rules!

Don't forget that there is a dedicated lesson for each integer rule. Just click the links above for more examples and step by step instruction!

Comparing and ordering integers can also be tricky. Visit our comparing and ordering integers page for more help!

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