Calculator Form
Use real numbers or integers. Choose the quotient rule that matches your class, software language, or reporting standard.
Example Data Table
| Dividend | Divisor | Mode | Integer Quotient | Remainder |
|---|---|---|---|---|
| 29 | 6 | Truncation | 4 | 5 |
| -29 | 6 | Truncation | -4 | -5 |
| -29 | 6 | Floor | -5 | 1 |
| -29 | -6 | Euclidean | 5 | 1 |
| 17.5 | 4 | Truncation | 4 | 1.5 |
Formula Used
Core Equations
- Exact quotient: qexact = a / b
- Remainder: r = a - bq
- Identity check: a = bq + r
- Remainder ratio: r / |b|
Integer Quotient Rules
- Truncation: q = trunc(a / b)
- Floor: q = floor(a / b)
- Euclidean: q = floor(a / b) for positive b, otherwise q = ceil(a / b), giving 0 ≤ r < |b|.
How to Use This Calculator
- Type the dividend and divisor values.
- Choose truncation, floor, or Euclidean division.
- Set the display precision for rounded output.
- Press Calculate Now to place the result above the form.
- Review the cards, working table, and graph.
- Export the finished result as CSV or PDF.
FAQs
1) What is the quotient?
The quotient is the result of dividing one number by another. This page shows both the exact quotient and the integer quotient used to build the remainder.
2) What is the remainder?
The remainder is the leftover part after using an integer quotient. It is calculated from the identity r = a - bq.
3) Why do negative inputs change the answer?
Negative numbers interact differently with truncation, floor, and Euclidean rules. The chosen quotient rule decides whether the remainder can be negative or must stay nonnegative.
4) Can I enter decimals?
Yes. The calculator accepts integers and decimals. The exact quotient stays continuous, while the selected integer rule determines the quotient used for the remainder formula.
5) What is Euclidean division?
Euclidean division forces the remainder into the range 0 ≤ r < |divisor|. Many math texts prefer this form because the remainder stays nonnegative.
6) When should I use floor division?
Use floor division when your course, algorithm, or data rule defines the quotient as the greatest integer less than or equal to a / b.
7) How do I verify the output quickly?
Multiply the divisor by the displayed integer quotient, then add the remainder. The result should rebuild the original dividend, except for tiny rounding display effects.
8) Why export CSV or PDF?
CSV is useful for spreadsheets and batch records. PDF is useful for reports, homework submissions, and sharing a fixed snapshot of the calculation.