A division with a remainder
987 ÷ 12 = 82 remainder 3, or 82¼ as a mixed number, or 82.25 as a decimal.
Long division calculator
Result
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How it works
Starting from the leftmost digit of the dividend, each step brings down the next digit, asks how many times the divisor fits into the number formed so far, records that as the next quotient digit, and carries the remainder into the next step. The process is identical whether the division comes out even or leaves a remainder.
The result is given three ways: quotient and remainder, a mixed number (quotient plus the remainder as a fraction, reduced to lowest terms), and a decimal — three views of exactly the same division.
Formulas used
The division identity
Dividend = Divisor × Quotient + Remainder, with 0 ≤ Remainder < Divisor
Worked examples
A division with no remainder
144 ÷ 12 = 12 exactly, with no remainder.
Assumptions and limits
- Both the dividend and divisor are whole numbers.
- The divisor must be positive.
Frequently asked questions
What is the difference between the remainder and the decimal form?
The remainder is a whole number left over after dividing as far as whole numbers go; the decimal form instead keeps dividing into tenths, hundredths and so on to express that same leftover amount as a fraction of the divisor.
Why does the mixed number use the remainder over the divisor?
Because the remainder represents "however many divisor-sized pieces are left," so remainder ÷ divisor is exactly the fractional part still owed — reduced to lowest terms for a cleaner answer.
Can the dividend be smaller than the divisor?
Yes — the quotient will be 0 and the entire dividend becomes the remainder, since the divisor does not fit into it even once.
Does this work with negative numbers?
This calculator works with non-negative whole numbers, matching how long division is taught step by step — for negative inputs, divide the absolute values and apply the sign to the result afterward.
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