Key takeaways
- Long division repeats four steps in order: Divide, Multiply, Subtract, Bring down (DMSB).
- The mnemonic "Does McDonald's Sell Cheeseburgers?" reminds students of the four steps and their order.
- It is usually introduced in Grade 4–5 (Year 5–6), once students are fluent with their times tables.
- Line every digit up by place value — most mistakes come from columns drifting, not from the maths.
- Always check the answer: quotient × divisor + remainder should equal the original dividend.
Long division is the standard written method for dividing a larger number by a one- or two-digit divisor when mental maths and short division run out of room. It looks intimidating on the page, but it is really just one short loop repeated: divide, multiply, subtract, bring down, then start again with the next digit. Students who can recite that loop and keep their columns straight can divide almost any number.
Before you start, make sure everyone shares the vocabulary. In 754 ÷ 3, the 754 is the dividend (the number being shared), the 3 is the divisor (how many groups), the answer on top is the quotient, and anything left over is the remainder. Getting these four words solid early saves a lot of confusion later.
The four steps of long division (DMSB)
- 1
Divide
Look at the first digit of the dividend (or the first two if the first is too small). Ask how many times the divisor fits into it, and write that number above the line, directly over the digit you used.
- 2
Multiply
Multiply the digit you just wrote by the divisor and write the product underneath the digits you are working with. This is where quick times-table recall pays off.
- 3
Subtract
Subtract that product from the digits above it. The result must be smaller than the divisor; if it isn't, your quotient digit was too small.
- 4
Bring down
Bring down the next digit of the dividend next to your subtraction result, then return to Divide. Repeat until there are no digits left to bring down.
The classic classroom mnemonic for that order is "Does McDonald's Sell Cheeseburgers?" — Divide, Multiply, Subtract, Bring down. Some teachers add a fifth word, Repeat ("Does McDonald's Sell Cheeseburgers Regularly?"), to stress that the loop keeps going. In the UK the same layout is often called the bus stop method because the divisor and dividend sit inside a shape like a bus shelter.
A worked example: 754 ÷ 3
Work left to right, one digit at a time:
- Divide: 3 goes into 7 twice (2 × 3 = 6), so write 2 above the 7.
- Multiply & subtract: 2 × 3 = 6; 7 − 6 = 1.
- Bring down the 5 to make 15. 3 goes into 15 exactly five times, so write 5 above the 5. 5 × 3 = 15; 15 − 15 = 0.
- Bring down the 4 to make 4. 3 goes into 4 once, so write 1 above the 4. 1 × 3 = 3; 4 − 3 = 1 left over.
There are no more digits to bring down, so the answer is 251 remainder 1. Check it: 251 × 3 = 753, and 753 + 1 = 754. It matches the dividend, so the answer is correct.
Three ways to handle the remainder
Leave it as a remainder
Write '251 r1'. Best for early practice and for real problems where a leftover can't be split — like 754 pencils shared into 3 boxes leaves 1 spare.
Write it as a fraction
The remainder becomes the numerator and the divisor the denominator: 754 ÷ 3 = 251 1/3. This bridges neatly into your fractions unit.
Continue into decimals
Add a decimal point and zeros to the dividend and keep dividing: 754 ÷ 3 = 251.33… Useful once students meet money and measurement.
The mistakes students make most
Nearly every long-division error is one of these five, and none of them is really about division:
- Columns drift. A quotient digit ends up over the wrong place and the whole answer shifts. Grid paper or squared paper fixes this faster than any reteach.
- Forgetting a zero in the quotient. When the divisor doesn't fit into a brought-down digit, students skip it instead of writing a 0. For example,
618 ÷ 3 = 206— 3 into 1 is zero, so a 0 must sit above the 1. Miss it and you get 26. - Weak times tables. If recall of the divisor's multiples is shaky, every Multiply step becomes a guess. Fluency work is the real fix.
- Stopping too early. Students forget to bring down the final digit and hand in a partial answer.
- A subtraction result bigger than the divisor. That always means the quotient digit was too small — go back up one.
The point where U.S. Common Core (4.NBT.B.6) expects students to divide up to four-digit numbers by one-digit divisors.
Source: Common Core State Standards for Mathematics
An alternative: partial quotients
If a student is drowning in the standard algorithm, try partial quotients first. Instead of finding the exact digit each time, students subtract easy multiples of the divisor and keep a running tally. For 754 ÷ 3, a student might subtract 200 threes (600), then 50 threes (150), then 1 three (3), and add 200 + 50 + 1 = 251 with 1 left over. It takes more lines but far less pressure on exact place value, and it builds the number sense that makes the standard method click later.
Turn any long-division skill into a worksheet
Pick the divisor size, remainders or no remainders, and the number of questions — get a printable practice sheet with an answer key in seconds.
Make long division worksheets with AIFrequently asked questions
Teach the DMSB loop with the mnemonic 'Does McDonald's Sell Cheeseburgers?' and have students work on squared paper so their columns stay aligned. Start with divisors that go in evenly (no remainder), then introduce remainders, then two-digit divisors.
It is usually introduced in Grade 4 or 5 in the U.S. (Year 5 or 6 in the UK, NZ and Australia), after students are fluent with multiplication facts. Standard 4.NBT.B.6 expects dividing four-digit numbers by one-digit divisors.
Divide as normal until you have brought down the last digit. Whatever is left after the final subtraction — if it is smaller than the divisor — is the remainder. Write it as 'r' plus the number, as a fraction over the divisor, or continue with decimals.
Divide, Multiply, Subtract, and Bring down — then repeat the loop with the next digit until there is nothing left to bring down. Many teachers use the phrase 'Does McDonald's Sell Cheeseburgers?' to remember the order.
Multiply the quotient by the divisor, then add any remainder. If the result equals the original dividend, the answer is correct. For 754 ÷ 3 = 251 r1, check 251 × 3 = 753, plus 1 equals 754.