Integer Operations Calculator
How It Works
Type two integers, pick add, subtract, multiply, or divide, and the calculator applies the sign rule that matches your operation. It shows the answer alongside the rule it used, so you can compare your own reasoning against it. The two rules that trip students up most are the addition rules (same sign versus different sign) and the double-negative in subtraction, so the tool spells out which one fired on each calculation.
The basic rule:
- Same signs multiply/divide → Positive
- Different signs multiply/divide → Negative
- a - b = a + (-b)
- a - (-b) = a + b
Use this to check homework and to build a feel for the sign rules. Once you can predict the sign before the calculator shows it, you have the rule down. Zero is neither positive nor negative, and dividing by zero has no answer at all.
Frequently Asked Questions
How do I add two integers with different signs, like −7 + 3?
When the signs differ, subtract the smaller distance-from-zero from the larger, then keep the sign of the number that was farther from zero. For −7 + 3, the distances are 7 and 3; subtract to get 4, and since −7 is farther from zero the answer is negative: −7 + 3 = −4. When the signs are the same you do the opposite — add the two amounts and keep the shared sign, so −7 + −3 = −10.
Why does a negative times a negative equal a positive, like −6 × −4 = 24?
A negative sign flips direction. Multiplying by one negative flips the sign once; multiplying by a second negative flips it back, so you land on positive. That is why −6 × −4 = 24 rather than −24. Multiplication and division follow the same shortcut: same signs give a positive result, different signs give a negative result. It is the only way the numbers stay consistent with the distributive property that governs regular multiplication.
How do I subtract a negative number?
Subtracting a negative is the same as adding the opposite, so the two minus signs become a plus: a − (−b) = a + b. For example, 5 − (−3) = 5 + 3 = 8. A number line makes it concrete — subtracting moves left, but subtracting a negative reverses that and moves you right, toward larger values.
What is the sign rule for dividing integers, like −20 ÷ 5?
Division uses the exact same sign rule as multiplication: same signs give a positive quotient, different signs give a negative one. In −20 ÷ 5 the signs differ, so the answer is negative: −20 ÷ 5 = −4. If both were negative, such as −20 ÷ −5, the quotient would be positive 4.
What are integers, and does this calculator handle decimals?
Integers are whole numbers and their negatives, including zero: ..., −3, −2, −1, 0, 1, 2, 3, ... They never include fractions or decimals. The sign rules on this page apply to any signed numbers, but this tool is built for practicing integer operations, so stick to whole numbers to match the worked examples.
Is there a quick way to remember all the sign rules?
For multiplying and dividing: matching signs make a positive, mismatched signs make a negative — count the negative signs, and an even count is positive while an odd count is negative. For adding: same signs add and keep that sign, different signs subtract and take the sign of the number farther from zero. For subtracting: rewrite it as adding the opposite, then use the addition rules.