Add, Subtract, Multiply, and Divide Integers

Integers are whole numbers, which means they are not fractions or decimals. Integers include positive whole numbers (1, 2, 3, ...), negative whole numbers (-1, -2, -3, ...), and zero (0).

• **Same Signs:** Add the absolute values and keep the common sign.
  Example: 5 + 3 = 8; -5 + (-3) = -8
• **Different Signs:** Subtract the smaller absolute value from the larger absolute value. The answer takes the sign of the integer with the larger absolute value.
  Example: 5 + (-3) = 2; -5 + 3 = -2

To subtract integers, you can "add the opposite". Change the subtraction sign to an addition sign and change the sign of the second integer to its opposite. Then follow the rules for addition.

Example: 5 - 3 = 5 + (-3) = 2

Example: 3 - 5 = 3 + (-5) = -2

Example: -5 - 3 = -5 + (-3) = -8

Example: -5 - (-3) = -5 + 3 = -2

• **Same Signs:** The product is positive.
  Example: 5 × 3 = 15; -5 × (-3) = 15
• **Different Signs:** The product is negative.
  Example: 5 × (-3) = -15; -5 × 3 = -15

The rules for division signs are the same as for multiplication signs (assuming the divisor is not zero):

• **Same Signs:** The quotient is positive.
  Example: 15 ÷ 3 = 5; -15 ÷ (-3) = 5
• **Different Signs:** The quotient is negative.
  Example: 15 ÷ (-3) = -5; -15 ÷ 3 = -5

Division by zero is undefined.

The set of integers is "closed" under addition, subtraction, and multiplication. This means that when you add, subtract, or multiply any two integers, the result will always be another integer.

However, the set of integers is **not** closed under division. Dividing one integer by another may result in a fraction or decimal that is not an integer (e.g., 5 ÷ 2 = 2.5). The result of integer division is only guaranteed to be an integer if the dividend is a multiple of the divisor.