When dealing with positive and negative numbers, it’s essential to understand the rules that govern how these numbers interact during the basic arithmetic operations of addition, subtraction, multiplication, and division. Here’s a detailed look at each operation:
Addition
- Positive + Positive = Positive: When you add two positive numbers, the result is always positive. For example, 3 + 5 = 8.
- Negative + Negative = Negative: Adding two negative numbers results in a negative number. For instance, -3 + (-5) = -8.
- Positive + Negative or Negative + Positive: The result’s sign depends on the larger absolute value. If |5| > |3|, then 5 + (-3) = 2. But if we reverse, -5 + 3 = -2.
Subtraction
- Positive – Positive: Positive minus positive can be positive, negative, or zero depending on the numbers. For example, 5 – 3 = 2, but 3 – 5 = -2.
- Negative – Negative: When subtracting a negative from a negative, it can result in either positive or negative. For instance, -5 – (-3) = -2.
- Positive – Negative: Subtracting a negative number is like adding a positive. So, 5 – (-3) = 5 + 3 = 8.
- Negative – Positive: This will yield a negative number. For example, -5 – 3 = -8.
Multiplication
- Positive x Positive = Positive: Multiplying two positive numbers always gives a positive result. For example, 4 x 5 = 20.
- Negative x Negative = Positive: The product of two negative numbers is positive. For instance, -4 x -5 = 20.
- Positive x Negative or Negative x Positive: The product of a positive and a negative number is negative. For example, 4 x -5 = -20 and -4 x 5 = -20.
Division
- Positive ÷ Positive = Positive: Dividing two positive numbers yields a positive result. For example, 10 ÷ 2 = 5.
- Negative ÷ Negative = Positive: Similar to multiplication, the division of two negative numbers gives a positive number. For instance, -10 ÷ -2 = 5.
- Positive ÷ Negative or Negative ÷ Positive: Dividing a positive by a negative or a negative by a positive results in a negative outcome. For example, 10 ÷ -2 = -5 and -10 ÷ 2 = -5.
Understanding these rules is crucial for working with numbers in mathematics, as they help simplify problems and enhance numerical fluency.