What is (-3) + (-5)?
The Question
Find the value of (-3) + (-5).
This looks tricky at first because of the minus signs, but once you understand the rule, it becomes very easy.
Understanding What Negative Numbers Mean
Think of the number line. Positive numbers are to the right of zero, and negative numbers are to the left.
← -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 →Negative numbers represent things like:
- Floors below ground level (B1 = -1, B2 = -2)
- Temperature below 0°C (like -3°C in Shimla)
- Money you owe someone (a debt of ₹5 = -5)
So (-3) + (-5) could mean: “I’m already ₹3 in debt, and I borrow another ₹5. How much do I owe now?”
The Rule for Adding Two Negative Integers
When both integers have the same sign (both negative):
- Add the values (ignore the minus signs for now).
- Keep the negative sign in the answer.
(-a) + (-b) = -(a + b)
Both negative → Add values → Put a negative sign on the answer.
Step-by-Step Solution
Problem: (-3) + (-5)
Step 1: Both numbers are negative — same sign rule applies.
Step 2: Add the values (ignoring the signs for now):
3 + 5 = 8
Step 3: Put the negative sign back:
Answer = -8
So, (-3) + (-5) = -8
Visualising on the Number Line
The number line makes this very clear.
Start at -3 on the number line.
Now we are adding -5, which means we move 5 steps to the left (negative direction).
← -9 -8 -7 -6 -5 -4 -3 -2 -1 0 →
←←←←←
land hereStarting at -3, moving 5 steps left: -3, -4, -5, -6, -7, -8.
We land on -8. Confirmed!
Debt/Credit Analogy
Let’s use a money example:
You owe your friend ₹3 (you’re “at -3”). Today you borrow another ₹5 from them (adding -5 more).
Total debt = ₹3 + ₹5 = ₹8
Since both are debts, you now owe ₹8 in total. That’s -8.
Verification
We can verify using the commutative property: the order of addition doesn’t matter for integers.
(-5) + (-3) = -(5 + 3) = -8 ✓
Same answer!
Common Mistake to Avoid
Many students write (-3) + (-5) = -2 or +2.
This happens when students confuse addition with subtraction.
(-3) + (-5) is NOT (-3) - (-5).
When we ADD two negatives, the debt grows bigger, not smaller. The answer must be MORE negative than both original numbers.
-8 is less than both -3 and -5, which makes sense — the total debt is bigger than either individual debt.
Try These Similar Problems
Problem 1: (-4) + (-7) = ?
Both negative. Add values: 4 + 7 = 11. Keep negative sign. Answer: -11
Problem 2: (-10) + (-6) = ?
Both negative. Add values: 10 + 6 = 16. Keep negative sign. Answer: -16
Problem 3: The temperature on Monday was -4°C. By Tuesday it dropped by another 6°C. What is Tuesday’s temperature?
(-4) + (-6) = -(4 + 6) = -10°C
Tuesday’s temperature is -10°C.
Exam tip: In CBSE Class 7 exams, questions on adding negative integers often appear as word problems (temperature, floors, sea level). Remember the rule: same signs → add values → keep the sign. You can also draw a quick number line if you’re unsure.