Calculate the quotient, remainder, decimal, or fraction result of any division problem, with optional step-by-step long division.
Division Formula
Division splits a number into equal parts. The number you start with is the dividend, the number you divide by is the divisor, and the answer is the quotient.
quotient = dividend / divisor
When the divisor does not go in evenly, whole number division leaves a remainder. The dividend, divisor, quotient, and remainder are linked by this identity:
dividend = quotient * divisor + remainder
The same division can also be written as a fraction, which you can then simplify:
dividend / divisor = fraction (reduced)
- dividend: the number being divided.
- divisor: the number you divide by. It cannot be zero.
- quotient: the result of the division.
- remainder: what is left over when the divisor does not divide the dividend evenly.
The solve-for selector controls which form you get. Decimal mode returns the quotient as a decimal and rounds it to the number of places you choose, and for whole numbers it also shows the exact value, marking any repeating block in parentheses. Quotient and remainder mode returns whole number division as dividend = quotient times divisor plus remainder, and an optional toggle shows the full long division work. Fraction mode reduces the division to a simplified fraction and gives the mixed number when the top is larger than the bottom.
Division Terms and Result Forms
Use this to match each part of a division problem to its name and to see how one division can be written in different forms.
| Term | Meaning | In 17 / 5 |
|---|---|---|
| Dividend | Number being divided | 17 |
| Divisor | Number you divide by | 5 |
| Quotient | Whole number result | 3 |
| Remainder | Amount left over | 2 |
| Problem | Quotient and remainder | Decimal | Fraction |
|---|---|---|---|
| 17 / 5 | 3 remainder 2 | 3.4 | 17/5 = 3 2/5 |
| 10 / 4 | 2 remainder 2 | 2.5 | 5/2 = 2 1/2 |
| 22 / 7 | 3 remainder 1 | 3.142857… | 22/7 |
| 1 / 3 | 0 remainder 1 | 0.(3) | 1/3 |
The digits inside parentheses, such as 0.(3), repeat forever. This happens whenever the divisor has prime factors other than 2 and 5.
Examples
Example 1: quotient and remainder. Divide 1234 by 7. Seven goes into 12 one time (7), leaving 5. Bring down the 3 to make 53; seven goes in 7 times (49), leaving 4. Bring down the 4 to make 44; seven goes in 6 times (42), leaving 2. The quotient is 176 and the remainder is 2, so 1234 = (176 times 7) + 2.
Example 2: decimal and fraction. Divide 45 by 8. As a decimal, 45 / 8 = 5.625 exactly. As whole number division, 8 goes into 45 five times (40) with a remainder of 5, so the quotient is 5 remainder 5. As a fraction, 45/8 reduces no further and equals the mixed number 5 5/8.
Frequently Asked Questions
What is a remainder? The remainder is the amount left over when the divisor does not divide the dividend evenly. It is always smaller than the divisor. For example, 17 divided by 5 is 3 with a remainder of 2, because 3 times 5 is 15 and 17 minus 15 is 2.
How do I turn a remainder into a decimal or fraction? Put the remainder over the divisor. In 17 / 5, the remainder 2 over the divisor 5 gives the fraction 2/5, which as a decimal is 0.4, so the full answer is 3.4 or 3 2/5. Decimal mode does this for you and rounds to the number of places you set.
Why does the answer show digits in parentheses? Parentheses mark a repeating decimal. When a division never ends, one block of digits repeats forever, such as 0.(3) for 1 divided by 3 or 3.(142857) for 22 divided by 7. The calculator detects this for whole number inputs and shows the repeating block instead of cutting the number off.
