Adding and Subtracting Integers Calculator
Add and subtract positive and negative integers step by step, with the Keep-Change-Change rule for subtracting a negative and clear sign rules.
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Adding and subtracting integers
Integers are whole numbers that can be positive or negative. Adding and subtracting them comes down to a few sign rules and one handy shortcut for subtracting a negative.
The sign rules
- Same signs — add the values, keep the sign. −5 − 6 = −11.
- Different signs — subtract the smaller from the larger, take the larger sign. −13 + 5 = −8.
Tip: Picture a number line. Adding a positive moves right, adding a negative moves left. Subtracting flips the direction.
Keep, Change, Change
Subtracting a negative is the same as adding a positive:
- Keep the first number.
- Change the minus to a plus.
- Change the sign of the second number.
So 4 − (−3) = 4 + 3 = 7, and −10 − (−22) = −10 + 22 = 12.
Brackets group first
Brackets change the grouping, so they can change the answer:
- −10 − (−22 + 33) = −10 − 11 = −21
- −10 − −22 + 33 = −10 + 22 + 33 = 45
Worked example
−12 − 16 + −22 − (33 − 58) — first the bracket gives 33 − 58 = −25, then −12 − 16 + −22 − (−25) works left to right to −25.
Common mistakes
- Forgetting Keep-Change-Change when subtracting a negative.
- Reordering a chain of plus and minus instead of going left to right.
- Ignoring brackets that regroup the numbers.
For expressions that also use × ÷ or exponents, switch to the order of operations calculator.
Frequently asked questions
- How do you add two integers with the same sign?
- Add the values and keep the shared sign. Negative 5 plus negative 6 is negative 11, and 5 plus 6 is 11. Same signs stack up in that direction.
- How do you add integers with different signs?
- Subtract the smaller value from the larger and take the sign of the larger value. Negative 13 plus 5 is negative 8, because 13 is larger than 5 and it is negative.
- What is the Keep-Change-Change rule?
- It turns a subtraction of a negative into an addition. Keep the first number, change the minus sign to plus, and change the sign of the second number. So 4 minus negative 3 becomes 4 plus 3, which is 7.
- Is subtracting a negative the same as adding?
- Yes. Subtracting a negative number is the same as adding its positive. Negative 10 minus negative 22 is negative 10 plus 22, which is 12.
- How do brackets change an integer expression?
- Brackets are evaluated first, which can change the answer. Negative 10 minus the quantity negative 22 plus 33 is negative 10 minus 11, or negative 21 — different from negative 10 minus negative 22 plus 33, which is 45.
- Can I use multiplication or division here?
- No. This calculator handles only addition and subtraction of whole numbers. For expressions with multiplication, division, or exponents, use the order-of-operations calculator.
- Why does order matter with a chain of plus and minus?
- Addition and subtraction are done left to right. Reading them out of order, or mishandling a minus in front of a negative, is the most common source of wrong answers.