Adding & Subtracting Integers Calculator

Add or subtract up to 8 integers and get step-by-step working, a live number line, and full rule explanations — instantly.

Examples:

What Are Integers?

Integers are a set of numbers that include all whole numbers — both positive and negative — and zero. They are represented by the symbol ℤ (from the German word Zahlen, meaning "numbers").

ℤ = { …, −4, −3, −2, −1, 0, 1, 2, 3, 4, … }
Negative
…−3, −2, −1
Left of zero
Zero
0
Neither + nor −
Positive
1, 2, 3…
Right of zero
⚠ Integers do NOT include: fractions (½, ¾), decimals (3.14, −0.5), or imaginary numbers (√−1).

The Integer Number Line

−5 −4 −3 −2 −1 0 1 2 3 4 ← Negative direction Positive direction →

Rules for Adding & Subtracting Integers

+ Addition Rules

Rule 1 — Same Signs

Add the absolute values and keep the common sign.

3 + 5 = 8   (both positive → +)
(−3) + (−5) = −8   (both negative → −)
Rule 2 — Opposite Signs

Subtract the smaller absolute value from the larger. Keep the sign of the larger number.

(−3) + 5 = 2   (|5|>|−3|, keep +)
3 + (−5) = −2   (|−5|>|3|, keep −)

− Subtraction Rule — "Add the Opposite"

To subtract an integer, add its opposite. Change the subtraction sign to addition, then flip the sign of the number being subtracted.

a − b  =  a + (−b)
Subtracting a positive
5 − 3 = 5 + (−3) = 2
Subtracting a negative (double negative)
−5 − (−3) = −5 + 3 = −2

All 8 Integer Operation Combinations

Operation Type Rule Applied Example Result
Positive + Positive Add absolute values, keep + 3 + 4 7
Negative + Negative Add absolute values, keep − (−3) + (−4) −7
Positive + Negative Subtract, keep sign of larger 3 + (−4) −1
Negative + Positive Subtract, keep sign of larger (−3) + 4 1
Positive − Positive Add opposite: a + (−b) 3 − 4 −1
Negative − Negative Add opposite: a + b (double neg) (−3) − (−4) 1
Positive − Negative Add opposite: a + b (double neg) 3 − (−4) 7
Negative − Positive Add opposite: a + (−b) (−3) − 4 −7

Properties of Integer Addition

Commutative Property
a + b = b + a

Order doesn't matter for addition.

3 + (−5) = (−5) + 3 = −2
Associative Property
(a + b) + c = a + (b + c)

Grouping doesn't change the result.

(2+3)+(−4) = 2+(3+(−4)) = 1
Identity Property
a + 0 = a

Adding zero leaves a number unchanged.

(−7) + 0 = −7
Inverse Property
a + (−a) = 0

Every integer plus its opposite equals zero.

5 + (−5) = 0  |  −3 + 3 = 0
Closure Property
a + b ∈ ℤ   and   a − b ∈ ℤ

Adding or subtracting any two integers always produces another integer. The set is "closed" under these operations.

Worked Examples

All 8 operation types — click Try it to load any example into the calculator.

Addition — Same Signs

3 + 4 = 7
Pos + Pos
Both positive → add absolute values, keep + sign
|3| + |4| = 7 → +7
(−3) + (−4) = −7
Neg + Neg
Both negative → add absolute values, keep − sign
|−3| + |−4| = 7 → −7

Addition — Opposite Signs

3 + (−4) = −1
Pos + Neg
Opposite signs → |4| > |3|, subtract: 4−3=1, keep − (sign of larger)
Result: −1
(−3) + 4 = 1
Neg + Pos
Opposite signs → |4| > |−3|, subtract: 4−3=1, keep + (sign of larger)
Result: +1

Subtraction (Add the Opposite)

3 − 4 = −1
Pos − Pos
3 − 4 = 3 + (−4) → opposite signs, |4|>|3|
3 + (−4) = −1
(−3) − (−4) = 1
Neg − Neg
Double negative: −(−4) = +4
(−3) + 4 = +1
3 − (−4) = 7
Pos − Neg
Double negative: −(−4) = +4
3 + 4 = +7
(−3) − 4 = −7
Neg − Pos
(−3) − 4 = (−3) + (−4) → both negative
−3 + (−4) = −7

Multi-Step & Real-World

Temperature Change

The temperature is −3°C. It rises 8°C, then drops 5°C. What is the final temperature?

−3 + 8 − 5 = ?
Step 1: −3 + 8 = 5
Step 2: 5 − 5 = 0
Final temperature: 0°C
Bank Account Balance

Balance: ₹500. Withdraw ₹200, deposit ₹350, withdraw ₹400. Final balance?

500 − 200 + 350 − 400
500 − 200 = 300 → 300 + 350 = 650 → 650 − 400 = 250
Final balance: ₹250

Frequently Asked Questions

What is an integer?

An integer is any whole number — positive, negative, or zero — with no fractional or decimal part. The set of integers is ℤ = {…, −3, −2, −1, 0, 1, 2, 3, …}. Numbers like 2.5, ½, and √2 are not integers.

How do you add integers with the same sign?

Add the absolute values of both numbers and give the result the common sign. If both are positive, the result is positive. If both are negative, the result is negative. Example: (−4) + (−6) = −10 because |−4| + |−6| = 10, and both have the negative sign.

How do you add integers with opposite signs?

Subtract the smaller absolute value from the larger, then use the sign of the number with the larger absolute value. Example: 5 + (−8): |−8| > |5|, so 8 − 5 = 3, and the result takes the sign of −8 → result is −3.

What does "subtracting a negative" mean?

Subtracting a negative number is the same as adding a positive — the two minus signs cancel: a − (−b) = a + b. Example: 4 − (−3) = 4 + 3 = 7. Think of it as "taking away a debt," which gives you more money.

What is the absolute value?

The absolute value of a number is its distance from zero on the number line — always non-negative. Written as |n|. Examples: |5| = 5, |−7| = 7, |0| = 0. Absolute value ignores the sign and tells you "how far" from zero.

What is a number's opposite (additive inverse)?

The opposite of a number is the same number with the sign flipped. Adding a number and its opposite always gives zero: a + (−a) = 0. The opposite of 6 is −6. The opposite of −9 is 9. The opposite of 0 is 0.

Does the order of addition matter for integers?

For addition, no — the commutative property says a + b = b + a. You can add integers in any order and get the same result. For subtraction, yes — order matters. 5 − 3 = 2 but 3 − 5 = −2. However, subtraction can always be rewritten as addition, and then the commutative property applies.