Understanding the rules for positive and negative numbers in mathematical operations helps to enhance your arithmetic skills significantly. Here’s a breakdown based on each operation:
Addition
- Positive + Positive: The result is always positive. For example, 3 + 2 = 5.
- Negative + Negative: The result is always negative. For example, -3 + (-2) = -5.
- Positive + Negative: Subtract the smaller absolute value from the larger absolute value. The sign of the result is determined by the sign of the number with the larger absolute value. For example, 5 + (-3) = 2, and -5 + 3 = -2.
Subtraction
- Positive – Positive: If the larger number is positive, the result is positive; if the larger number is negative, the result is negative. For example, 5 – 3 = 2 and 3 – 5 = -2.
- Negative – Negative: This is similar to addition but switch to the opposite signs. The result turns positive if you subtract from a smaller value. For example, -3 – (-2) = -3 + 2 = -1.
- Positive – Negative: Subtracting a negative is like adding a positive. For example, 5 – (-3) = 5 + 3 = 8.
- Negative – Positive: This results in moving further left on the number line. For example, -5 – 3 = -8.
Multiplication
- Positive × Positive: The result is positive. For example, 4 × 3 = 12.
- Negative × Negative: The result is also positive. For example, -4 × -3 = 12.
- Positive × Negative: The result is negative. For example, 4 × -3 = -12.
- Negative × Positive: The result is again negative. For example, -4 × 3 = -12.
Division
- Positive ÷ Positive: The result is positive. For example, 6 ÷ 2 = 3.
- Negative ÷ Negative: The result is positive. For example, -6 ÷ -2 = 3.
- Positive ÷ Negative: The result is negative. For example, 6 ÷ -2 = -3.
- Negative ÷ Positive: The result is again negative. For example, -6 ÷ 2 = -3.
By understanding and mastering these rules, you will feel more confident in your mathematical abilities and be able to approach problems involving positive and negative numbers with ease!