Understanding how to work with positive and negative numbers is essential for mastering arithmetic. Here are the basic rules:
1. Addition
- Positive + Positive: The result is positive. For example, 3 + 2 = 5.
- Negative + Negative: The result is negative. For example, -3 + (-2) = -5.
- Positive + Negative: Subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value. For example, 5 + (-3) = 2.
2. Subtraction
- Positive – Positive: If the first number is larger, the result is positive. If the second number is larger, the result is negative. For example, 5 – 3 = 2, but 2 – 5 = -3.
- Negative – Negative: This is the same as addition of absolute values. For example, -3 – (-2) = -3 + 2 = -1.
- Positive – Negative: This is the same as addition. For example, 5 – (-3) = 5 + 3 = 8.
- Negative – Positive: Essentially, it’s like adding. For example, -5 – 3 = -5 + (-3) = -8.
3. Multiplication
- Positive × Positive: The result is positive. For example, 4 × 3 = 12.
- Negative × Negative: The result is positive. For example, -4 × -3 = 12.
- Positive × Negative: The result is negative. For example, 4 × -3 = -12.
- Negative × Positive: The result is also negative. For example, -4 × 3 = -12.
4. Division
- Positive ÷ Positive: The result is positive. For example, 12 ÷ 3 = 4.
- Negative ÷ Negative: The result is positive. For example, -12 ÷ -3 = 4.
- Positive ÷ Negative: The result is negative. For example, 12 ÷ -3 = -4.
- Negative ÷ Positive: The result is also negative. For example, -12 ÷ 3 = -4.
These rules help simplify calculations when dealing with positive and negative numbers. Remembering the signs and how they interact is key to handling more complex math problems.