vmbo havo vwo
Division with remainder
Quick answer
dividend = divisor × quotient + remainder, with 0 ≤ remainder < divisor. Example: 17 ÷ 5 = 3 remainder 2, because 5 × 3 + 2 = 17.
Divisor 0 is not allowed. Use whole numbers of 0 or greater. In Dutch school books this is delen met rest — rest means remainder; deeltal / deler mean dividend / divisor.
Calculator
Enter dividend and divisor. You get quotient, remainder, and the check divisor × quotient + remainder = dividend.
What is division with remainder?
With whole numbers the divisor fits a certain number of times into the dividend; what is left over is the remainder. The quotient is that number of times. That is not the same as the decimal division 17 ÷ 5 = 3.4 on the online calculator. For sin, log or π use the scientific calculator.
| Term | Meaning | For 17 ÷ 5 |
|---|---|---|
| Dividend | The number you divide (Dutch: deeltal) | 17 |
| Divisor | What you divide by (≥ 1) (Dutch: deler) | 5 |
| Quotient | How many times the divisor fits | 3 |
| Remainder | What is left (0 ≤ remainder < divisor) (Dutch: rest) | 2 |
Always check: divisor × quotient + remainder = dividend. Writing the remainder as a fraction: fraction calculator. Euclid steps for gcd: GCD and LCM.
Examples by level
On vmbo (more practical track), havo and vwo (middle and university-preparatory tracks) the same identity holds.
17 sweets, 5 per bag. How many bags and how many left over?
- Quotient5 fits 3 times into 17
- Remainder17 − 15 = 2
- Check5 × 3 + 2 = 17
Three full bags, two sweets left over.
20 ÷ 4. Is there a remainder?
- Quotient5
- Remainder0
- Meaning20 is a multiple of 4
Why is the remainder always smaller than the divisor?
- DefinitionIf remainder ≥ divisor, the divisor still fits once more
- Consequence0 ≤ remainder < divisor
- UniqueFor fixed dividend and divisor > 0 the pair (quotient, remainder) is unique
Common mistakes
Wrong
Treating 17 ÷ 5 as 3.4 and calling that “remainder 4”
Right
3.4 is decimal. With remainder: 3 remainder 2. The remainder is not a digit after the decimal point.
Wrong
Dividing by 0
Right
The divisor must be a whole number ≥ 1.
Wrong
Writing remainder 5 when the divisor is 5
Right
Then 5 fits once more: quotient +1, remainder 0.
Wrong
Skipping the check
Right
Verify: divisor × quotient + remainder = dividend.
Practice
vmbo 23 ÷ 4. Quotient and remainder?
5 remainder 3
4 × 5 = 20; leftover 23 − 20 = 3. Verify: 4 × 5 + 3 = 23.
havo 36 ÷ 9.
4 remainder 0
36 is a multiple of 9.
havo 100 ÷ 7. Quotient and remainder?
14 remainder 2
7 × 14 = 98; leftover 100 − 98 = 2. Verify: 7 × 14 + 2 = 100.
vwo Why may the remainder not be 5 when the divisor is 5?
Then 5 still fits once more
Remainder 5 with divisor 5 means: quotient one higher, remainder 0.
In the Netherlands
Division with remainder belongs with whole numbers on vmbo and stays useful as a check for multiples on havo and vwo. The same remainder appears in the Euclidean algorithm for the gcd: GCD and LCM calculator. Simplifying fractions: fractions.
Next step
- How does this work? The explanation and examples are further up this page.
Learning path
- Related: GCD and LCM calculator · Fraction calculator
Frequently asked questions
What is division with remainder?
dividend = divisor × quotient + remainder, with 0 ≤ remainder < divisor. 17 ÷ 5 = 3 remainder 2, because 5 × 3 + 2 = 17.
What is the difference from ordinary division?
On the online calculator 17 ÷ 5 = 3.4 (decimal). Here you stay with whole numbers: 3 remainder 2. The remainder is not a digit after the decimal point.
When is the remainder 0?
When the divisor divides the dividend exactly, for example 20 ÷ 4 = 5 remainder 0. Then the dividend is a multiple of the divisor.
May the divisor be 0?
No. Division by 0 is not possible. The divisor must be a whole number ≥ 1.
Why may the remainder not be greater than or equal to the divisor?
If remainder ≥ divisor, the divisor still fits once more. Raise the quotient and lower the remainder until 0 ≤ remainder < divisor.