Integer arithmetic calculator covering addition, subtraction, multiplication, and division with positive and negative numbers. Includes sign rules and a number-line visualization.
Four tabs: addition and subtraction (four sign combinations with explanations), multiplication and division (full sign rules), order of operations (BODMAS / PEMDAS), and visual number line plus a reference table.
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Calculator information
📋 How to use this calculator
- Choose the operation: addition, subtraction, multiplication, or division.
- Enter two integers (positive or negative), for example -7 and 4.
- Click Calculate to see the result with an explanation of the sign rules involved.
- For multi-step expressions (BODMAS/PEMDAS), use the expression tab and enter something like '-3 + 4 x (-2)'.
- Use the Number Line tab for a visual representation of addition and subtraction.
- Refer to the sign-rule reference table for multiplication and division as a study aid.
🧮 Integer arithmetic rules
Addition: a + b; Subtraction: a - b = a + (-b); Sign rules for multiplication/division: (+)(+) = +, (-)(-) = +, (+)(-) = -, (-)(+) = -
- a, b = integers (Z = {..., -2, -1, 0, 1, 2, ...})
- Division requires b != 0
- PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
Dividing two integers does not always produce an integer (e.g., 7/2 = 3.5). Floor division (integer division) is common in programming.
💡 Worked example: Multi-step expression: -3 + 4 x (-2) - 6 / (-3)
Given:- Expression: -3 + 4 x (-2) - 6 / (-3)
- Rule: PEMDAS
Steps:- Step 1 (multiplication): 4 x (-2) = -8
- Step 2 (division): 6 / (-3) = -2
- Substitute: -3 + (-8) - (-2)
- Step 3 (left-to-right addition): -3 + (-8) = -11
- Step 4: -11 - (-2) = -11 + 2 = -9
Result: Final answer = -9
❓ Frequently asked questions
Why does a negative times a negative equal a positive?
Multiplying by -1 reverses direction on the number line, so reversing twice returns to the original direction. Algebraically: (-a)(-b) = -1 x a x -1 x b = (-1)^2 x ab = ab. It is also required to keep the distributive law a(b+c) = ab+ac consistent when a or b is negative.
What is the difference between integers and natural numbers?
Natural numbers (N) = {1, 2, 3, ...} or {0, 1, 2, 3, ...} depending on convention. Integers (Z, from the German Zahlen) include negatives, zero, and positives: {..., -2, -1, 0, 1, 2, ...}. Whole numbers = {0, 1, 2, 3, ...}. Every natural number is an integer, but not vice versa.
What are PEMDAS and BODMAS, and are they the same?
They are the same order-of-operations rule with different acronyms. PEMDAS (US): Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. BODMAS (UK): Brackets, Orders, Division, Multiplication, Addition, Subtraction. Multiplication and division share priority (left to right), as do addition and subtraction.
Is 0 positive or negative?
Zero is neutral - neither positive nor negative. It is the additive identity (a + 0 = a) and the multiplicative annihilator (a x 0 = 0). Division by 0 is undefined because no number times 0 equals a nonzero result. In some contexts (real analysis), zero is treated as non-negative.
How can I quickly add a long list of negative numbers?
Group positives and negatives separately, sum each, then combine. Example: -3 + 5 - 7 + 2 - 4 = (5+2) + (-3-7-4) = 7 + (-14) = -7. For long arithmetic series with a pattern, use S = n/2 x (a+L) where n = number of terms, a = first term, L = last term.
📚 Sources & references
Last updated: May 11, 2026