Long division: step by step, with examples
TutorAura guide · Updated
Long division breaks a big division into small steps you repeat until you run out of digits:
- Divide: how many times does the divisor go into the current number?
- Multiply: multiply the divisor by that answer.
- Subtract: take it away to find the remainder.
- Bring down: bring down the next digit and repeat.
A memory aid some families use: "Does McDonald's Sell Burgers?" (divide, multiply, subtract, bring down).
Key takeaways
- Repeat divide, multiply, subtract, bring down.
- Write a 0 in the answer when the divisor doesn't fit.
- Remainders can become decimals by adding .0 to the number.
- Check by multiplying: divisor × answer + remainder = original.
Example 1: 742 ÷ 7
- 7 goes into 7 once. , remainder 0.
- Bring down 4: 7 goes into 4 zero times. Write 0 in the answer; remainder 4.
- Bring down 2: 7 goes into 42 six times exactly.
Answer: 106. Check: . The zero in the middle is the step people skip; leave it out and you'd get 16.
Example 2: a remainder (1,234 ÷ 5)
- 5 doesn't go into 1, so start with 12: 5 goes in 2 times (), remainder 2.
- Bring down 3 to make 23: 4 times (), remainder 3.
- Bring down 4 to make 34: 6 times (), remainder 4.
Answer: 246 remainder 4. Check: .
As a decimal: write 1,234 as 1,234.0 and bring down the 0: 5 goes into 40 eight times, so .
Example 3: a two-digit divisor (3,288 ÷ 24)
Writing out the first few multiples of 24 helps: 24, 48, 72, 96, 120, 144, 168, 192.
- 24 goes into 32 once; remainder 8.
- Bring down 8 to make 88: 3 times (), remainder 16.
- Bring down 8 to make 168: 7 times exactly.
Answer: 137. Check: .
Long division vs short division
Short division (the "bus stop" method) does the same steps, but you carry remainders as small digits instead of writing out each subtraction. It's quicker for one-digit divisors. Long division is clearer for two-digit divisors and for decimals, because every subtraction is visible.
In the US, fluent division of multi-digit numbers with the standard algorithm is expected by grade 6; in England, formal written division is taught in upper key stage 2.
Common mistakes
- Missing a 0 in the answer when the divisor doesn't fit.
- Misaligning columns, so digits are brought down to the wrong place.
- A remainder bigger than the divisor, which means the last step's answer was too small.
- Forgetting to check by multiplying back.
Practice
- (give a remainder)
Answers: 214, 105, 125, 157 remainder 5. For a quick drill on the facts that make division easy, try the times tables quiz.
Frequently asked questions
What is the difference between long and short division?
They use the same steps. In long division you write out each multiplication and subtraction under the number; in short division you work them out in your head and carry the remainder as a small digit. Short division is quicker for one-digit divisors; long division is clearer for bigger ones.
What if the divisor won't go into the first digit?
Use the first two digits instead, and don't write anything above the first digit (or write a 0). For 156 ÷ 6, 6 doesn't go into 1, so start with 15: that's 2 remainder 3. Bring down the 6 to make 36, which is 6. The answer is 26.
What are the steps of long division?
Divide, multiply, subtract, bring down, then repeat until there are no digits left to bring down. Whatever is left at the end is the remainder.
How do you turn a remainder into a decimal?
Put a decimal point after the number and add zeros (1,234 becomes 1,234.0), then keep dividing. Put a decimal point in the answer directly above the one in the number.
How can I check a long division answer?
Multiply the answer by the divisor and add the remainder. If you get the original number back, the division is right.
Sources
- National curriculum in England: mathematics programmes of study. Department for Education.
- Common Core State Standards for Mathematics. Common Core State Standards Initiative.
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