Math
Remainder Calculator
Enter a dividend and a divisor to find the whole-number quotient and the remainder, then see the same answer written as a mixed number, a reduced fraction, and a decimal.
The check line proves the result, and negative inputs show both the truncated (calculator) and floored (Python) remainders so you can match whatever convention your class uses.
The number being divided.
The number you divide by. Cannot be 0.
Try an example
Result
Quotient and remainder
—
- Quotient
- —
- Remainder
- —
- Mixed number
- —
- Fraction (reduced)
- —
- Decimal
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the remainder calculator solves
Enter a dividend and a divisor to find the whole-number quotient and the remainder, then see the same answer written as a A whole number written next to a fraction, like 2 1/3., a reduced fraction, and a decimal. The check line proves the result, and negative inputs show both the truncated (calculator) and floored (Python) remainders so you can match whatever convention your class uses.
Formula
How to use it
- Enter the dividend (the number being divided) and the divisor.
- Read the quotient and remainder, then the same value as a mixed number, reduced fraction, and decimal.
- Use the check line, divisor × quotient + remainder = dividend, to verify.
How to read the answer
The quotient counts how many whole times the divisor fits; the remainder is what is left and is always smaller than the divisor in size. The mixed number puts the remainder over the divisor, the fraction reduces the whole division, and the decimal continues dividing. For negative inputs, most calculators (and this page's main answer) keep the remainder's sign equal to the dividend's; Python instead keeps it equal to the divisor's.
Common mistakes and edge cases
- Writing a remainder equal to or larger than the divisor; the quotient should be one bigger.
- Confusing the remainder with the decimal part: 47 ÷ 6 = 7.833…, but the remainder is 5, not 0.833.
- Reducing the mixed number's fraction incorrectly: 47 ÷ 6 = 7 5/6 already in lowest terms, but 48 ÷ 10 = 4 8/10 = 4 4/5.
- Assuming remainders of negative numbers are always positive; the convention decides.
- Dividing by 0.
Worked examples
47 ÷ 6
7 R 5, or 7 5/6 ≈ 7.8333.
Quotient and remainder
7 R 5
Exact division 84 ÷ 12
Remainder 0.
Quotient and remainder
7 R 0
Dividend smaller than divisor
3 ÷ 8 = 0 R 3.
Quotient and remainder
0 R 3
Negative dividend
-47 ÷ 6 = -7 R -5 (truncated); floored gives -8 R 1.
Quotient and remainder
-7 R -5
Large numbers
Exact with 15-digit inputs.
Quotient and remainder
142,857,142,857,142 R 5
Division by zero
Undefined.
Quotient and remainder
Error
Frequently asked questions
What is the remainder of 47 divided by 6?+
5. Six fits into 47 seven times (42), and 47 - 42 = 5. As a mixed number that is 7 5/6.
How do I turn a remainder into a decimal?+
Divide the remainder by the divisor and add it to the quotient: 5 ÷ 6 = 0.8333…, so 47 ÷ 6 = 7.8333….
How do I write a division with remainder as a mixed number?+
The quotient is the whole part and the remainder over the divisor is the fraction: 47 ÷ 6 = 7 5/6. Reduce the fraction if possible.
Can a remainder be negative?+
Under the truncated convention used by most calculators and languages like C and JavaScript, -47 ÷ 6 gives remainder -5. Under floored division (Python, math class) the remainder is 1. Both satisfy 6 × q + r = -47.
Can the remainder be bigger than the divisor?+
No. If it is, the divisor fits at least one more time, so increase the quotient.
What is the difference between remainder and modulo?+
They agree for positive numbers. For negatives, 'remainder' usually means the truncated version and 'modulo' the floored version; the modulo calculator shows both.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026