Free · Arithmetic
Integer Operations with Worked Results
Add, subtract, multiply, divide, exponentiate, take roots or logarithms of integer operands with a visible calculation and real-domain checks.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
For a = 8 and b = 2, addition gives 10. Changing the operation preserves both operands.
a+b; a−b; a×b; a/b; a^b; real bth root of a; log(a)/log(b).
Worked example
Enter these known values and leave the other values blank.
- a
- 8
- b
- 2
- Result
- 8 + 2 = 10
Assumptions and limitations
- Enter integer operands; negative values and zero are allowed where the selected operation is defined. Division, roots, logarithms and negative powers may produce noninteger results.
- Division requires a nonzero divisor. Real logarithms require a positive argument and positive base other than one. Root degree is a nonzero integer; a negative radicand requires an odd degree.
- Arithmetic uses finite numerical precision. Noninteger roots and logarithms are approximations; very large powers may exceed representable precision or finite output limits. All seven captured result fields retain their supported inverse input paths through the API, including noninteger results that derive valid integer operands. The visible result note follows the selected operation.
- Use decimal or scientific notation, or arithmetic expressions whose intermediate steps preserve all digits in this calculator. Unsupported functions, noninteger powers, nonterminating division, values outside the numeric range and expressions beyond the verifier’s work limits are rejected. Enter a supported decimal value instead; the tool checks the original entry before ordinary64-digit arithmetic.
- Supplied inverse results must describe an exact integer-operand relation that the bounded verifier can prove. All seven inverse paths remain, including noninteger division and logarithm results. A proof may reject a very large exponent, a fractional logarithm with large numerator or denominator, a conflicting locked value, or a relation that loses digits. Clear the inverse result and enter the original integer operands when it cannot be verified. Ordinary forward roots and logarithms remain approximations.
Common questions
Will every answer be an integer?
Enter integer operands; negative values and zero are allowed where the selected operation is defined. Division, roots, logarithms and negative powers may produce noninteger results.
Can I take a root of a negative integer?
An odd, nonzero integer degree has a real signed root. An even degree does not give a real root of a negative number.
References
Use the real signed root for a negative radicand and odd integer degree; retain every captured inverse and all other operations. Require exact integer operands and operation-specific real arithmetic domains while preserving seven selectable operations and hidden results. Preserve all integer operands and seven supported result inverses while proving admitted raw numeric entry is an exact finite decimal before ordinary evaluation. Reject lossy or unsupported expressions with actionable decimal-entry guidance; retain every operation domain. Reuse source-pinned scientific display for finite tiny values without changing arithmetic precision.