Do Two Negatives Make a Positive When Subtracting? Math Explained
Why Two Negatives Don't Always Equal a Positive
Here's the thing most people never actually learned properly in school: two negatives do not automatically make a positive. It depends entirely on the operation you're performing.
When you're adding negative numbers, two negatives can indeed become more negative. When you're multiplying or dividing, two negatives do produce a positive. But the rule isn't universal, and conflating these operations is where most of the confusion comes from.
How Subtraction Actually Works with Negatives
Subtraction is the operation you're asking about, so let's break it down properly. The key concept here is that subtracting a negative is the same as adding its positive counterpart.
Think of it this way: subtracting removes something. If you have -5 and you subtract -3, you're removing negative 3 from negative 5. Removing a negative brings you closer to positive territory.
The Double Negative Rule in Subtraction
When you see two negative signs in a row during subtraction, they cancel each other out. Here's the pattern:
- 5 - (-3) becomes 5 + 3, which equals 8
- -7 - (-2) becomes -7 + 2, which equals -5
- -4 - (-4) becomes -4 + 4, which equals 0
The two negatives don't make a positive on their own. They cancel, and then you perform the addition operation with whatever numbers remain.
When Two Negatives DO Make a Positive
Two negatives making a positive happens in multiplication and division, not subtraction. This is a different rule entirely.
- (-3) × (-4) = 12 ✅ Two negatives make a positive
- (-10) ÷ (-2) = 5 ✅ Two negatives make a positive
- 5 - (-3) = 8 ❌ This is subtraction, not multiplication
Why Multiplication Is Different
Multiplication deals with groups and scaling. When you multiply two negative numbers, you're essentially reversing direction twice, which lands you in positive territory. It's about the relationship between the numbers, not simple addition or removal.
Common Mistakes and How to Avoid Them
People routinely mix up these rules. Here's where it goes wrong:
Mistake #1: Assuming Subtraction Follows Multiplication Rules
If you see 3 - (-5) and think "two negatives make a positive, so that's 3 + 5 = 8," you got the right answer, but for the wrong reason. The actual process is: subtracting a negative means you're adding. So 3 - (-5) = 3 + 5 = 8.
Mistake #2: Confusing the Signs
Students often write 5 - (-3) = 5 - -3 and then get confused. Always convert the double negative into a single positive operation immediately. Write it as 5 + 3 from the start.
Visualizing the Number Line
If you're still struggling, visualize it on a number line. 🧮
Starting at zero, moving left is negative direction, moving right is positive direction. When you subtract, you move left. When you subtract a negative, you move left by a negative amount—which means you move right instead.
It's counterintuitive, but that's exactly why the rule exists: subtracting a negative moves you in the positive direction.
Quick Reference Table
| Operation | Example | Result | Two Negatives = Positive? |
|---|---|---|---|
| Subtraction | 5 - (-3) | 8 | No — they cancel, then you add |
| Addition | -5 + (-3) | -8 | No — stays negative |
| Multiplication | (-5) × (-3) | 15 | Yes |
| Division | (-10) ÷ (-2) | 5 | Yes |
Practical How To: Solving Double Negative Problems
Here's your step-by-step process for handling any expression with two negatives:
Step 1: Identify the Operation
Is it subtraction, multiplication, or division? This determines everything.
Step 2: For Subtraction Only
Convert any instance of "minus a negative" into "plus a positive." Change the double negative to a single positive sign.
Step 3: For Multiplication/Division
Count the negative signs. An even number of negatives gives you a positive result. An odd number gives you a negative result.
Step 4: Calculate
Perform the operation with the simplified signs.
Example Walkthrough
Solve: -12 - (-8)
- It's subtraction ✅
- Convert: -12 - (-8) becomes -12 + 8
- Calculate: -12 + 8 = -4
The Bottom Line
Two negatives make a positive only in multiplication and division. In subtraction, they cancel each other out and become a positive sign, which means you switch from subtraction to addition.
Memorize the difference. It will save you from making avoidable errors on tests and in real calculations. There's no trick here—just different rules for different operations.