A negative plus a negative is not a positive; it is negative. Take this: -3 + -5 = -8. When you add two negative numbers, you are combining amounts that both move in the same direction: away from zero on the negative side of the number line Not complicated — just consistent..
What Does “Negative Plus a Negative” Mean?
A negative number is a number less than zero. It can represent a debt, a loss, a temperature below freezing, a movement to the left, or a value below a starting point. When you add a negative number to another number, you are usually moving left on the number line.
Real talk — this step gets skipped all the time Easy to understand, harder to ignore..
For example:
- 3 + -2 = 1
- 3 - 2 = 1
- -3 + -2 = -5
The key idea is that adding a negative number has the same effect as subtracting a positive number. In math, this is why the expression -4 + -6 can also be written as -4 - 6. Both expressions mean you start at negative four and move six more steps in the negative direction.
The Simple Rule
The rule for adding two negative numbers is very simple:
When you add two negative numbers, add their absolute values and keep the negative sign.
For example:
-7 + -2
Step 1: Add the numbers without the negative signs:
7 + 2 = 9
Step 2: Keep the negative sign:
-9
So:
-7 + -2 = -9
Another example:
-10 + -15
Add the numbers:
10 + 15 = 25
Keep the negative sign:
-25
So:
-10 + -15 = -25
This rule works because both numbers are pulling the result in the same direction: toward zero’s opposite side, which is the negative side Easy to understand, harder to ignore..
Visualizing It on a Number Line
A number line is a helpful way to understand why a negative plus a negative is negative.
Imagine a number line:
- Numbers to the right of zero are positive.
- Numbers to the left of zero are negative.
- Zero is the starting point.
If you start at -3 and add -4, you move 4 spaces to the left Most people skip this — try not to. Turns out it matters..
That takes you from:
-3 → -4 → -5 → -6 → -7
So:
-3 + -4 = -7
You do not cross into positive numbers. Instead, you move farther away from zero in the negative direction.
This is different from adding two positive numbers, where you move farther to the right. It is also different from adding a positive and a negative number, where the numbers may cancel each other out.
Why Isn’t the Answer Positive?
Many people think the answer might be positive because multiplying two negatives gives a positive result. For example:
-3 × -2 = 6
That rule is true for multiplication, but it does not apply to addition. Addition and multiplication follow different rules.
When you add two negative numbers, you are not “canceling” the negatives. You are combining them.
For example:
-2 + -3 = -5
Both numbers are negative, so the result becomes more negative.
A useful way to think about it is this:
Negative plus negative means “more of the same kind of negative.”
If you already owe $5 and then borrow another $8, you now owe $13. That can be written as:
-5 + -8 = -13
The result is not positive because both amounts are debts Nothing fancy..
Real-Life Examples
Negative plus negative appears often in real life.
Temperature
If the temperature is -4°C and it drops another 6°C, what is the new temperature?
You can write this as:
-4 + -6 = -10
The temperature becomes 10 degrees below zero Most people skip this — try not to. That's the whole idea..
Money and Debt
If you have -$20 in your account and spend another $15, your balance changes like this:
-20 + -15 = -35
You are now $35 below zero.
Elevators and Depth
Suppose you are in an elevator at floor -3 and go down another 5 floors.
You can write:
-3 + -5 = -8
You are now at floor -8.
These examples show that negative plus negative is not only a math rule; it also describes real situations involving losses, drops, debts, and downward movement Turns out it matters..
Difference Between Adding and Subtracting Negative Numbers
One of the most common mistakes is confusing addition with subtraction.
For example:
-4 + -6 = -10
But:
-4 - -6 = 2
Why?
Because subtracting a negative number is the same as adding a positive number:
-4 - -6 = -4 + 6 = 2
So the signs matter a lot.
Here are some important examples:
- -5 + -3 = -8
- -5 - -3 = -2
- 5 + -3 = 2
- 5 - -3 = 8
A helpful reminder is:
Adding a negative moves left. Subtracting a negative moves right.
Common Mistakes to Avoid
Many students make the same mistakes when working with negative numbers. Here are a few important ones Worth knowing..
Mistake 1: Thinking the Answer Is Always Positive
Some people see two negative signs and assume the answer is positive. That is true for multiplication and division, but not for addition.
Correct:
-6 + -4 = -10
Incorrect:
-6 + -4 = 10
Mistake 2: Forgetting to Keep the Negative Sign
When adding negative numbers, do not ignore the negative signs.
Correct:
-8 + -2 = -10
Incorrect:
-8 + -2 = 6
Mistake 3: Confusing Addition with Subtraction
The expression -7 - -4 is different from -7 + -4.
Correct:
-7 + -4 = -11
Correct:
-7 - -4 = -3
The difference is small in writing but large in meaning Most people skip this — try not to..
Quick Practice Examples
Try these examples:
- -2 + -9 = -11
- -6 + -1 = -7
More Practice Problems
Try solving these on your own, then check your answers at the end of the section.
- -12 + ‑7 = ?
- -3 + ‑15 = ?
- -9 + ‑4 = ?
- -1 + ‑19 = ?
- -25 + ‑5 = ?
Answers
- -19 (-12 + ‑7 = -(12 + 7) = -19)
- -18 (-3 + ‑15 = -(3 + 15) = -18)
- -13 (-9 + ‑4 = -(9 + 4) = -13)
- -20 (-1 + ‑19 = -(1 + 19) = -20)
- -30 (-25 + ‑5 = -(25 + 5) = -30)
Tips for Working with Negative Numbers
| Tip | Why It Helps |
|---|---|
| Combine the absolute values first | Adding negatives is like adding debts; you can add the magnitudes and then apply the negative sign. |
| Keep the sign visible | Write the “‑” next to each number throughout the calculation to avoid accidentally dropping it. |
| Use a number line for intuition | Moving left on the line represents adding a negative; visualizing the distance reinforces the result. |
| Check subtraction carefully | Remember that “‑ ‑” becomes “+”. Rewrite the expression before solving to reduce errors. |
| Practice with real‑world contexts | Relating problems to temperature drops, debt, or depth makes the abstract rule concrete. |
Quick Reference: Adding Negative Numbers
-
Rule: (-a + (-b) = -(a + b))
(Add the magnitudes, keep the negative sign.) -
Special case: If one of the numbers is zero, (-a + 0 = -a).
-
Contrast with subtraction: (-a - (-b) = -a + b)
(Subtracting a negative flips the sign of the second term.)
Final Takeaway
Adding two negative numbers always yields a more negative result because you are accumulating quantities that are already less than zero. By treating the absolute values as “amounts of negativity” and then applying the negative sign, you can handle these problems quickly and accurately. Mastering this concept not only strengthens your arithmetic skills but also improves your ability to interpret real‑world situations involving loss, debt, and decline.
To wrap this up, remember that “negative plus negative” means “more of the same kind of negative.” Keep the signs clear, practice regularly, and you’ll confidently figure out any scenario where numbers dip below zero Worth knowing..
