Integers
Integers include positive whole numbers, negative whole numbers, and zero.
The “set of all integers” is often shown like this:
Integers = {… -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …}
The dots at each end of the set mean that you can keep counting in either direction. The set can also be shown as a number line:
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The arrows on each end of the number line mean that you can keep counting in either direction.
Adding and Subtracting Integers
Looking at a number line can help you when you need to add or subtract integers.
Whether you are adding or subtracting two integers, start by using the number line to find the first number. Put your finger on it. Let's say the first number is 3.
- Then, if you are adding a positive number, move your finger to the right as many places as the value of that number. For example, if you are adding 4, move your finger 4 places to the right.
3 + 4 = 7
- If you are adding a negative number, move your finger to the left as many places as the value of that number. For example, if you are adding -4, move your finger 4 places to the left.
3 + -4 = -1
- If you are subtracting a positive number, move your finger to the left as many places as the value of that number. For example, if you are subtracting 4, move your finger 4 places to the left.
3 - 4 = -1
- If you are subtracting a negative number, move your finger to the right as many places as the value of that number. For example, if you are subtracting -4, move your finger 4 places to the right.
3 - -4 = 7
Here are two rules to remember:
- Adding a negative number is just like subtracting a positive number.
3 + -4 = 3 - 4
- Subtracting a negative number is just like adding a positive number. The two negatives cancel out each other. WE USE THE RULE: Keep. Change. Change.
3 + 4 = 3 - -4
Multiplying and Dividing Integers
If you multiply or divide two positive numbers, the result will be positive.
6 x 2 = 12
6 / 2 = 3
If you multiply or divide a positive number with a negative number, the result will be negative.
6 x -2 = -12
6 / -2 = -3
If you multiply or divide two negative numbers, the result will be positive—the two negatives will cancel out each other.
-6 x -2 = 12
-6 / -2 = 3
Is It an Integer?
Integers are whole numbers and their negative opposites. Therefore, these numbers can never be integers:
- fractions
- decimals
- percents
