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Negative Numbers Calculator

Add, subtract, multiply and divide with negative numbers — with every sign rule explained step by step. Covers all combinations of positive and negative inputs so you can see why the answer is positive or negative, not just what it is.

Negative numbers calculator

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Step by step calculations

Addition with negatives

Negative Numbers Calculator Explained

Core concepts, classroom applications, and plain-English explanations for all audiences.

Where you already use negative numbers

The weather app shows −3°C. Your bank account goes into overdraft — that's a negative balance. Death Valley sits at −86 metres below sea level. A golfer who is 4 under par is at −4. Negative numbers describe anything that goes below zero or in the opposite direction.

Worked example

"The temperature at midnight was −5°C. By noon it rose 9°C. What was the noon temperature?"

Start: −5°C

Add 9: −5 + 9

= 9 − 5 (the positive is larger)

Result: +4°C at noon

Tip: picture a number line — start at −5, move 9 steps right.

The rule that trips everyone up

  • ✗ "Two negatives always make a positive": Only for × and ÷. Adding two negatives makes a bigger negative: (−3) + (−4) = −7, not +7.

Subtracting a negative = adding

5 − (−3) = 5 + 3 = 8. Think of it as removing a debt: if someone cancels a £3 debt you owe, you're £3 better off.

The rules explained

Working with negative numbers

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Adding negatives
Adding a negative number is the same as subtracting its magnitude. Think of it as moving left on a number line. Adding two negatives always gives a more negative result — you add the magnitudes and keep the minus sign.
5 + (−3) = 5 − 3 = 2
(−4) + (−3) = −(4+3) = −7
(−4) + 6 = 6 − 4 = 2
(−1) + 1 = 0
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Subtracting negatives
Subtracting a negative is the same as adding — two minus signs combine into a plus. Think of it as "removing a debt". This is the rule students most commonly get wrong — the double negative in subtraction becomes positive.
5 − (−3) = 5 + 3 = 8
(−4) − (−3) = −4 + 3 = −1
(−2) − (−5) = −2 + 5 = 3
a − (−b) = a + b
×÷
Multiplying & dividing negatives
The sign rules for multiplication and division are the same. Same signs give a positive result; different signs give a negative result. Multiply (or divide) the magnitudes as normal, then apply the sign rule.
AopB=
+×÷++
−×÷−+
+×÷−−
−×÷+−
!
Common mistake
"Two negatives make a positive" — only sometimes
This rule only applies to multiplication and division. Students often incorrectly apply it to addition, thinking (−3) + (−4) = +7. That is wrong — adding two negatives makes a bigger negative. The double-negative rule only applies when the two negatives interact through × or ÷.
(−3) × (−4) = +12 ✓ two negatives → positive

(−3) + (−4) = −7 ✓ still negative!
(−3) + (−4) ≠ +7 ✗ a very common error