Division with remainders answers two questions at once: how many whole times does one number go into another, and how much is left over? 17 ÷ 5 is 3 remainder 2, because 5 goes into 17 three whole times (15) with 2 left over. Every remainder must be smaller than the number you are dividing by; if it is not, the number goes in at least once more. This guide shows the quick mental method, the long-division layout for bigger numbers, the three ways to write the answer, and how to decide what to do with a remainder in a word problem. For any pair of numbers, the division calculator shows the quotient, the remainder and every step.
In 17 ÷ 5 = 3 r 2, 17 is the dividend (the amount being shared), 5 is the divisor (the size of each group), 3 is the quotient (how many whole groups) and 2 is the remainder (what is left). They always fit this check:
divisor × quotient + remainder = dividend → 5 × 3 + 2 = 17
Use that line to check every answer. It catches almost every slip.
For small numbers, count up in the divisor's times table until the next step would overshoot. To find how many times 8 goes into 15: 8, 16. 16 is too big, so 8 goes into 15 once, remainder 7 (15 − 8 = 7).
Knowing your times tables to 12 makes this instant. If any table is slow, the times tables chart and the Missing Factor game, which asks exactly "what times 7 makes 56?", are the fastest fix.
| Question | Answer | Check |
|---|---|---|
| How many times does 6 go into 36? | 6 exactly | 6 × 6 = 36 |
| How many times does 16 go into 80? | 5 exactly | 16 × 5 = 80 |
| How many times does 8 go into 15? | 1, remainder 7 | 8 × 1 + 7 = 15 |
| How many times does 3 go into 16? | 5, remainder 1 | 3 × 5 + 1 = 16 |
| How many times does 7 go into 50? | 7, remainder 1 | 7 × 7 + 1 = 50 |
| How many times does 12 go into 100? | 8, remainder 4 | 12 × 8 + 4 = 100 |
Take 289 ÷ 13. 13 does not go into 2, so look at 28: 13 × 2 = 26, write 2, and 28 − 26 = 2. Bring down the 9 to make 29: 13 × 2 = 26 again, write 2, and 29 − 26 = 3. No digits are left, so 289 ÷ 13 = 22 r 3. Check: 13 × 22 + 3 = 286 + 3 = 289. ✓
Now 576 ÷ 49. 49 does not go into 5, but it goes into 57 once (49), leaving 8. Bring down 6 to make 86: 49 goes in once more, leaving 37. So 576 ÷ 49 = 11 r 37. Check: 49 × 11 + 37 = 539 + 37 = 576. ✓
Our long division explained guide covers the layout, the chunking method and where people usually go wrong.
For the mixed number, the remainder goes over the divisor: r 20 when dividing by 140 is 20/140, which simplifies to 1/7. For the decimal, keep dividing after the decimal point by adding zeros to the dividend. Which form to use depends on the question: whole objects want r, measurements usually want a decimal, and exact answers in algebra usually want a fraction.
| Division | With r | As a mixed number | As a decimal |
|---|---|---|---|
| 17 ÷ 5 | 3 r 2 | 3 2/5 | 3.4 |
| 289 ÷ 13 | 22 r 3 | 22 3/13 | 22.2308… |
| 576 ÷ 49 | 11 r 37 | 11 37/49 | 11.7551… |
| 300 ÷ 140 | 2 r 20 | 2 1/7 | 2.142857… |
Round up when everything must be included. 30 people, 8 per car: 30 ÷ 8 = 3 r 6, so you need 4 cars.
Round down when only complete groups count. $30 buys how many $8 tickets? 3 r 6, so 3 tickets with $6 change.
Use the remainder when the question is about what is left. 30 sweets shared between 8 children: each gets 3 and 6 are left over.
Use a decimal when the amount can be split. 30 litres into 8 bottles: 3.75 litres each.
Reading the question for one of these four cases is often harder than the division itself, and it is where many test marks are lost.
Dividing by 2: odd numbers leave remainder 1.
Dividing by 5 or 10: the last digit tells you. 47 ÷ 5 leaves 2; 47 ÷ 10 leaves 7.
Dividing by 3 or 9: add the digits. 524 has digit sum 11, and 11 ÷ 3 leaves 2, so 524 ÷ 3 leaves remainder 2. The same works for 9: 11 ÷ 9 leaves 2.
Dividing by 4: only the last two digits matter. 1,234: 34 ÷ 4 = 8 r 2, so 1,234 ÷ 4 leaves 2.
Exactly 6 times with no remainder, because 6 × 6 = 36.
Once, with a remainder of 7, because 8 × 1 = 8 and 15 − 8 = 7.
11 remainder 37. 49 × 11 = 539, and 576 − 539 = 37. As a decimal it is about 11.755.
No. If it is equal to or bigger than the divisor, the divisor fits in at least once more, so increase the quotient and subtract again.
Divide the remainder by the divisor. 17 ÷ 5 = 3 r 2, and 2 ÷ 5 = 0.4, so the answer is 3.4.
Count up in the divisor's times table, stop before you overshoot, and what is left is the remainder. Check every answer with divisor × quotient + remainder = dividend, and pick r, a fraction or a decimal to suit the question. For big numbers the division calculator shows each step; for speed, drill the tables with Missing Factor.