Whether I am teaching a math course, tutoring a group of students or working one on one with a student, I’ve realized that working with signed numbers can cause students much grief when performing calculations. I wanted to take a brief moment to add a few helpful hints that can help students remember the rules when it comes to working with signed numbers.

### Rules for Adding Signed Numbers:

Question: Do the numbers have the same sign?

- Answer: Yes ⇒ Find the sum and keep the sign
- 5 + 9 = 14
- (-5) + (-9) = -14
- Answer: Yes ⇒ Find the sum and keep the sign
- 5 + (-9) = -4 or (-9) + 5 = -4
- (-5) + 9 = 4 or 9 + (-5) = 4

### Rules for Subtracting Signed Numbers:

Subtraction is adding the opposite sign of the second number

- 5 – 9 → 5 + (-9) = -4
- 5 – (-9) → 5 + 9 = 14
- -5 – 9 → -5 + (-9) = -14
- -5 – (-9) → -5 + 9 = 4

### Multiplication and Division of Signed Numbers:

Multiplying and Dividing signed numbers follow the same rules

Rules for Multiplication

- Positive x Positive = Positive: 3 x 4 = 12
- Negative x Negative = Positive: (-3) x (-4) = 12
- Negative x Positive = Negative: (-3) x 4 = -12
- Positive x Negative = Negative: 3 x (-4) = -12

Rules for Division

- Positive ÷ Positive = Positive: 12 ÷ 3 = 4
- Negative ÷ Negative = Positive: (-12) ÷ (-3) = 4
- Negative ÷ Positive = Negative: (-12) ÷ 3 = -4
- Positive ÷ Negative = Negative: 12 ÷ (-3) = -4