💡 How to Use This Lesson
Click any card above or use the tabs to navigate. Each lesson breaks down a concept step by step with visuals. The Number Line tab is interactive — you can try your own problems! Finish with the Quiz to test your GED readiness.
Same signs → Add the absolute values (ignore the sign while adding), then keep the common sign in the result.
Think of it as normal addition. (+7) + (+3): add 7 + 3 = 10, keep the + sign.
(-5) + (-8): ignore signs, add 5 + 8 = 13, then put the − sign back → −13.
What is (−4) + (−9)? (Both negative — add 4+9, keep the minus sign)
Different signs → Subtract the smaller absolute value from the larger one. Keep the sign of the number with the larger absolute value.
For (+9) + (−4): absolute values are 9 and 4.
9 − 4 = 5
9 is larger and it's positive (+9), so the answer is +5.
What is (−15) + (+6)? (15 > 6, and 15 is negative — so the answer is negative)
Change subtraction to addition, then flip the sign of the number being subtracted. Apply the addition rules from Lessons 1 & 2.
7 − (+3) becomes 7 + (−3)
7 + (−3): different signs, 7 − 3 = 4, 7 is larger and positive → +4
What is (−3) − (−8)? (Flip the second sign: −3 + 8 = ?)
Start at the first number. If adding a positive → move right. If adding a negative → move left. Where you land is the answer!
Enter these into the interactive tool above:
• (−3) + (+7) | (+5) + (−9) | (−4) + (−3)
Distance = |a − b| — subtract the two numbers and take the absolute value (always positive). Distance is never negative!
Distance = |16 − (−25)|
16 − (−25) = 16 + 25 = 41
|41| = 41 — the distance is always positive.
What is the distance between −8 and +12 on a number line? (Use |12 − (−8)| = ?)
| Operation | What To Do | Sign of Result |
|---|---|---|
| (+a) + (+b) | Add normally | Always + |
| (−a) + (−b) | Add normally | Always − |
| (+a) + (−b), a > b | Subtract: a − b | + |
| (+a) + (−b), b > a | Subtract: b − a | − |
| (+a) − (+b) | Rewrite as (+a) + (−b) | Depends on larger |
| (−a) − (−b) | Rewrite as (−a) + (+b) | Depends on larger |
| (+a) − (−b) | Rewrite as (+a) + (+b) → ADD! | Always + |
| (−a) − (+b) | Rewrite as (−a) + (−b) → ADD! | Always − |
| Distance |a − b| | Subtract, take absolute value | Always positive |
🔑 Key Memory Trick
Subtracting a negative = Adding a positive!
4 − (−6) = 4 + 6 = 10 — two negative signs side by side cancel out and become a plus!