A number and its opposite add to zero. 7 + (−7) = 0. They are additive inverses.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Every subtraction is an addition
5 − 3 is 5 + (−3). Both give 2, and the second form works for negatives too.
Why bother
Four separate rules for subtracting signed numbers collapse into one rule for adding them.
The case that needs it
−4 − (−9) becomes −4 + 9, which is 5. Written as a subtraction it invites guessing.
Every number has an opposite
The additive inverse of a number is what you add to reach zero: the inverse of 7 is −7, and of −7 is 7. Zero is its own inverse. This is the property that makes cancellation work.
Subtraction defined through it
a − b means a + (−b). Subtraction is not really a separate operation at all — it is addition of an inverse. Once you see it that way, all four sign cases collapse into the addition rules you already have.
Why this matters for equations
Solving x + 5 = 12 works by adding −5 to both sides, because 5 + (−5) = 0 clears the 5 away. Every "do the same to both sides" step is an inverse being applied. The property is doing the work, not the ritual.
Reading the minus sign
In −x, the minus means "the opposite of x", and if x is negative then −x is positive. The sign does not mean the value is negative. This trips people up constantly, and reading it as "the opposite of" rather than "minus" helps.
Step 2: Try It Yourself
Add two signed numbers and watch the movement on the line.
Adding 9 walks 9 to the right.
Step 3: Watch an Example
One step at a time.
Watch Ana Rewrite a Double Negative
Ana works out −4 − (−9).
- Step 1
She rewrites the subtraction as adding the opposite.
Step 4: Your Turn
Practice makes it stick.
The Rewrite
Problem 1 of 2
What is 6 − (−4)?
The Balance
Problem 2 of 2
A balance of −20 has a debt of 5 removed. What is the new balance?
Add the Opposite
1 of 4
3 − (−5) = ?
2 of 4
−7 − 2 = ?
3 of 4
−6 − (−6) = ?
4 of 4
What adds to 12 to give zero?
Step 5: Quick Check
Show what you know.
Question 1 of 1
−5 − (−8) = ?
What You Learned
- A number and its additive inverse add to zero.
- Every subtraction can be rewritten as adding the opposite.
- That turns several subtraction rules into one addition rule.