Integer operations calculator

What is an integer operations calculator?

The integer operations calculator adds, subtracts, multiplies, and divides whole numbers that may be positive or negative. Alongside the numeric answer it shows the operation rewritten in signed form, such as $(-5) + (+3) = -2$, so you can see exactly how the signs combine. It is a handy tool for students learning the rules of signs and for anyone who wants a quick, reliable check of an arithmetic step involving negative numbers.

How does the calculator work?

Enter the first integer, choose one of the four operations, and enter the second integer. The calculator immediately returns two things: the result of the operation and the same expression written with explicit signs and parentheses. Division by zero is undefined, so if you divide by zero the result is left empty.

Rules of signs

• Adding two numbers with the same sign: add their absolute values and keep the common sign.
• Adding two numbers with different signs: subtract the smaller absolute value from the larger and keep the sign of the larger.
• Subtracting a number is the same as adding its opposite: $a - b = a + (-b)$.
• Multiplying or dividing two numbers with the same sign gives a positive result.
• Multiplying or dividing two numbers with different signs gives a negative result.

Formulas

For two integers $a$ and $b$, the four basic operations are:

$a + b$ $a - b$ $a \times b$ $a \div b, \quad b \neq 0$

The result keeps the sign determined by the rules above, and for division the divisor $b$ must not be zero.

Worked examples

1. Addition: $(-5) + (+3) = -2$ The numbers have different signs, so subtract the absolute values ($5 - 3 = 2$) and keep the sign of the larger absolute value (negative), giving $-2$.

2. Subtraction: $(-8) - (-3) = -5$ Subtracting $-3$ is the same as adding $+3$, so $-8 + 3 = -5$.

3. Multiplication: $(-4) \times (+6) = -24$ The signs are different, so the product is negative: $-24$.

4. Division: $(-12) \div (-4) = 3$ The signs are the same, so the quotient is positive: $3$.

If the second integer is zero and the operation is division, the result is undefined, so the calculator shows no answer.

Practical notes

• Homework and revision: Check answers to signed-number exercises and confirm the rule of signs was applied correctly.
• Banking and budgeting: Combine credits (positive) and debits (negative) to find a net balance.
• Temperature and elevation: Work with values above and below a reference point, such as degrees below zero or depth below sea level.
• Programming: Verify the expected value of an integer expression before writing it in code.

Frequently asked questions

Why does subtracting a negative number make the result larger?

Subtracting a negative is the same as adding a positive, because $a - b = a + (-b)$. For example, $-8 - (-3) = -8 + 3 = -5$, which is greater than $-8$.

What sign does a product or quotient have?

Same signs give a positive result and different signs give a negative result. So $(-12) \div (-4) = 3$, while $(-4) \times (+6) = -24$.

What happens when I divide by zero?

Division by zero is undefined in ordinary arithmetic, so the calculator returns no result whenever the second integer is zero and the operation is division.

Does the calculator only work with integers?

The rules of signs shown here apply to any real numbers, but this tool is designed around whole-number (integer) inputs so the steps stay clear and easy to follow.