Rules for Integer Operations

Working with integers is all about following simple patterns. When adding integers with the same sign, add the numbers and keep the sign. For example, 5 + 2 = 7 or -5 + $-2$ = -7.

If the signs are different when adding, subtract the smaller absolute value from the larger one, then use the sign of the number with the larger absolute value. For example, -6 + 5 = -1 because |-6| is larger than |5|.

For subtracting integers, remember the "Keep-Change-Flip" method. Keep the first number, change the subtraction to addition, and flip the sign of the second number. Examples:

• -3 - 1 = -3 + $-1$ = -4
• -3 - $-8$ = -3 + 8 = 5
• 8 - 3 = 5

Quick Tip: Think of subtraction as "adding the opposite." Instead of subtracting 5, you're adding -5!

When multiplying or dividing integers, first do the operation with the absolute values. Then determine the sign: if both numbers have the same sign, the answer is positive. If they have different signs, the answer is negative.

Understanding Integers

Integers include all positive and negative whole numbers plus zero {...-3, -2, -1, 0, 1, 2, 3...}. Negative integers are less than zero and are written with a minus sign. Positive integers are greater than zero and can be written with or without a plus sign.

Zero is special—it's neither positive nor negative! When you graph integers on a number line, just place a dot at the appropriate position.

The absolute value of a number is the distance between that number and zero on a number line. Remember that distance is always positive, so |-5| = 5 and |5| = 5.

A helpful way to remember multiplication and division rules is with this visual:

• Positive × Positive = Positive (both eyes open = awake = good)
• Negative × Negative = Positive (both eyes closed = asleep = good)
• Positive × Negative = Negative (one eye open, one closed = hurt = negative)

Fun Fact: The word "integer" comes from the Latin word "integer" which means "whole" or "complete." Now you know why they're called whole numbers!