Adding and Subtracting Integers Calculator
Enter an equation with positive and negative integers — see every step of the work.
Add and Subtract Integers
Use numbers and operators + - and parentheses ( ). Negative numbers are fine: e.g. -10 - -22 + 33
Answer
Showing the Work
Calculator Use
This calculator solves addition and subtraction problems with positive and negative integers. Type your equation using numbers, +, -, and parentheses ( ). The calculator evaluates using standard PEMDAS order of operations and shows each simplification step.
Input Examples
| Input Style | Example | Answer | Notes |
|---|---|---|---|
| No parentheses | -10 – -22 + 33 | 45 | Double negatives handled |
| With parentheses | (-10) – (-22) + 33 | 45 | Same result |
| With grouping | -10 – (-22 + 33) | -21 | Group changes precedence |
| Multiple groups | (5 + -3) – (10 – 14) | 6 | Each group evaluated first |
| All negative | -5 – 3 – -8 – 12 | -12 | Negative running total |
Rules for Adding and Subtracting Integers
➕ Adding Integers
(−) + (−)Negative sum(+) + (+)Positive sum(−large) + (+small)Negative(+large) + (−small)PositiveWhen signs differ, subtract the smaller absolute value from the larger. Keep the sign of the larger.
➖ Subtracting Integers
(−) − (−) = (−) + (+)May be +(−) − (+) = (−) + (−)Negative(+) − (−) = (+) + (+)Positive(+) − (+) depends on sizeChange subtraction to addition and flip the sign of the number being subtracted. Then apply addition rules.
Worked Examples
-10 – -22 + 33
-10 – (-22 + 33)
-15 – -7 + -3 + 20
(5 + -3) – (10 – 14)
Understanding Integer Signs
| Pattern | Equivalent To | Example | Result | Why |
|---|---|---|---|---|
| a + b | Standard addition | 5 + 3 | 8 | Same signs — add |
| a + (−b) | a − b | 5 + (−3) | 2 | Adding a negative = subtract |
| a − b | Standard subtraction | 5 − 3 | 2 | Positive minus positive |
| a − (−b) | a + b | 5 − (−3) | 8 | Subtracting a negative = add |
| (−a) + (−b) | −(a + b) | −5 + (−3) | −8 | Both negative — sum is negative |
| (−a) − b | −(a + b) | −5 − 3 | −8 | Both moves left on number line |
| (−a) − (−b) | b − a | −5 − (−3) | −2 | Minus negative = plus positive |
Frequently Asked Questions
What are integers?
Integers are whole numbers — including positive numbers (1, 2, 3…), negative numbers (−1, −2, −3…), and zero. They do not include decimals or fractions. Together, positive and negative integers can represent direction and magnitude — think of bank balances, temperature change, floor levels in a building, or elevation.
Why does subtracting a negative give a positive?
Think of subtraction as “removing.” Removing a debt (a negative) is the same as gaining money. On the number line, subtracting negative moves you to the right (increasing), just like adding a positive. Formally: a − (−b) = a + b because the two negatives cancel.
Does PEMDAS mean multiplication always before division?
No — this is a common misreading. Multiplication and division have equal precedence and are evaluated left to right. Similarly, addition and subtraction are equal and evaluated left to right. PEMDAS just groups them into levels of precedence: (1) Parentheses, (2) Exponents, (3) Mult/Div left-to-right, (4) Add/Sub left-to-right.
Can I enter decimal numbers?
Yes — while decimals are technically not integers, this calculator accepts decimal inputs because users frequently mix them. The same sign rules apply: −3.5 − −1.2 = −3.5 + 1.2 = −2.3.
What’s the difference between − and a negative sign?
The minus sign (−) serves two roles: as a binary operator (5 − 3, meaning “subtract 3 from 5”) and as a unary sign (−3, meaning “negative three”). Context determines which it is. When you write 5 − −3, the first − is the operator and the second is the negative sign on 3. The calculator handles both forms correctly.
How do parentheses change the answer?
Parentheses force a sub-expression to be evaluated first. Compare: −10 − (−22 + 33) vs −10 − −22 + 33. In the first, −22 + 33 = 11 is computed before subtracting, giving −10 − 11 = −21. In the second, reading left-to-right: −10 + 22 + 33 = 45. Parentheses dramatically change the result.
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“Adding and Subtracting Integers Calculator” at TheCalculatorSoup.com — Online Calculators. Last updated: 2025.