1-2 3 Integers Explained
1. What are Integers?
Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals. The set of integers is represented as \( \mathbb{Z} \).
2. Positive Integers
Positive integers are whole numbers greater than zero. They are also known as natural numbers. Examples include 1, 2, 3, 4, and so on.
Example:
If you have 3 apples, the number 3 is a positive integer.
3. Negative Integers
Negative integers are whole numbers less than zero. They are represented with a minus sign. Examples include -1, -2, -3, -4, and so on.
Example:
If you owe someone 5 dollars, you can represent this as -5, which is a negative integer.
4. Zero
Zero is an integer that is neither positive nor negative. It is the only integer that is exactly in the middle of the number line.
Example:
If you have no apples, you have 0 apples, which is represented by the integer 0.
5. Operations with Integers
Integers can be added, subtracted, multiplied, and divided. The rules for these operations can be summarized as follows:
- Addition: When adding integers, if both numbers have the same sign, add their absolute values and keep the same sign. If they have different signs, subtract the smaller absolute value from the larger one and keep the sign of the larger absolute value.
- Subtraction: Subtracting an integer is the same as adding its opposite. For example, \( 5 - 3 \) is the same as \( 5 + (-3) \).
- Multiplication: The product of two integers with the same sign is positive. The product of two integers with different signs is negative.
- Division: The quotient of two integers with the same sign is positive. The quotient of two integers with different signs is negative.
Example:
Calculate \( 5 + (-3) \):
Since 5 and -3 have different signs, subtract the smaller absolute value (3) from the larger one (5): \( 5 - 3 = 2 \). Keep the sign of the larger absolute value, which is positive, so the answer is \( 2 \).