Remainder Calculator
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When a number does not divide evenly, the part left over is the remainder. 47 ÷ 5 = 9 R 2, because 5 × 9 = 45 and 47 − 45 = 2. The check is always dividend = divisor × quotient + remainder.
| Answer | |
| Quotient | 9 |
| Remainder | 2 |
| Written as | 9 R 2 |
| Decimal | 9.4 |
| Mixed number | 9 2⁄5 |
| Check | |
| Divisor × quotient + remainder | 5 × 9 + 2 = 47 |
Show steps
- How many times does 5 fit into 47? 9 times.
- 5 × 9 = 45.
- Remainder = 47 − 45 = 2.
- The remainder 2 is less than the divisor 5, so the division is done.
How to find a remainder
- Divide and keep only the whole-number part. That is the quotient.
- Multiply the divisor by the quotient.
- Subtract that from the dividend. What is left is the remainder.
Example: 100 ÷ 7. Seven fits 14 times (7 × 14 = 98). 100 − 98 = 2, so 100 ÷ 7 = 14 R 2. The remainder must always be smaller than the divisor.
Remainders as fractions and decimals
| Division | Quotient R remainder | Mixed number | Decimal |
|---|---|---|---|
| 47 ÷ 5 | 9 R 2 | 9 2⁄5 | 9.4 |
| 100 ÷ 7 | 14 R 2 | 14 2⁄7 | 14.2857… |
| 23 ÷ 4 | 5 R 3 | 5 3⁄4 | 5.75 |
| 36 ÷ 6 | 6 R 0 | 6 | 6 |
The remainder over the divisor is the fraction part of the answer.
Remainders in word problems
What you do with the remainder depends on the question. 30 students in vans that seat 8: 30 ÷ 8 = 3 R 6, so you need 4 vans (round up). 30 cookies shared by 8 children: each child gets 3 (drop the remainder) and 6 are left over. 30 feet of ribbon cut into 8 equal pieces: each piece is 3.75 ft (use the decimal).
Negative numbers and modulo
With negative numbers there are two common rules. In math, the remainder is usually kept between 0 and the divisor: −7 ÷ 3 = −3 R 2, because 3 × (−3) + 2 = −7. Many programming languages instead cut the quotient toward zero, giving −2 R −1. The calculator shows both.
Remainder practice questions
Test yourself with 6 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
If it were as big as the divisor, the divisor would fit one more time.
45 ÷ 4 = 11 R 1. The last person still needs a car, so round up to 12.
Quiz complete
Frequently asked questions
How do you calculate the remainder?
Find how many whole times the divisor fits into the dividend, multiply, and subtract from the dividend. For 38 ÷ 5: 5 × 7 = 35, and 38 − 35 = 3.
How do you turn a remainder into a decimal?
Divide the remainder by the divisor and add it to the quotient. 9 R 2 from 47 ÷ 5 is 9 + 2 ÷ 5 = 9.4.
What is the remainder when a smaller number is divided by a larger one?
The quotient is 0 and the remainder is the smaller number itself. 3 ÷ 8 = 0 R 3.
Is remainder the same as modulo?
For positive numbers, yes: 17 mod 5 = 2, the remainder of 17 ÷ 5. With negative numbers, different calculators and programming languages use different rules.
Sources
- Common Core State Standards: 4.NBT.B.6, whole-number quotients and remainders
- Wolfram MathWorld: Remainder
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