You can add any signed numbers. Subtracting turns out to be adding in disguise.
Key idea
Subtracting a number is the same as adding its opposite: $$a - b = a + (-b)$$ So $3 - (-5) = 3 + 5 = 8$, and $-4 - 6 = -4 + (-6) = -10$.
Why it works
Subtraction asks "how far from $b$ to $a$?" or "what do I add to $b$ to get $a$?" For $3 - (-5)$: from $-5$ to $3$ is 8 steps right, so the answer is $8$. With counters: to take 5 negative counters away from 3 positive ones, first add 5 zero pairs (that changes nothing), then remove the 5 negatives. Eight positives are left. Taking away a negative leaves you with more.
Worked examples
Worked example: Subtracting a negative
Find $3 - (-5)$.
- Add the opposite: $3 + 5$.
- $3 + 5 = 8$.
Answer: $8$
Worked example: Subtracting a positive
Find $-4 - 6$.
- Add the opposite: $-4 + (-6)$.
- Both negative: $-(4 + 6) = -10$.
Answer: $-10$
Worked example: A temperature difference
The high was $-2^\circ$F and the low was $-9^\circ$F. How much warmer was the high?
- Difference = high $-$ low: $-2 - (-9)$.
- Add the opposite: $-2 + 9 = 7$.
- Check on a thermometer: from $-9$ up to $-2$ is 7 degrees ✓.
Answer: 7 degrees
Common mistake
Treating "minus a negative" like "minus a positive," so that $3 - (-5)$ becomes $-2$. Remember the two changes: the minus sign becomes plus, and $-5$ becomes $5$. Check: subtraction undoes addition, so $8 + (-5)$ should give back $3$ ✓.