Long division is a tidy way to write partial quotients. Instead of chunks you choose, it divides one place at a time: hundreds, then tens, then ones.
Key idea
Repeat four moves for each place: divide, multiply, subtract, bring down. Write each quotient digit above the place you just divided. If a place is too small to share, write 0 there and bring down the next digit.
Why it works
In $618 \div 6$, the 6 hundreds share into 6 groups as 1 hundred each. The 1 ten cannot be shared into 6 groups, so each group gets 0 tens. That 0 holds the tens place, just like the 0 in 103. The 1 ten joins the 8 ones to make 18 ones, and $18 \div 6 = 3$.
Worked example: A zero in the quotient
Find $618 \div 6$.
- Hundreds: $6 \div 6 = 1$. Write 1. $1 \times 6 = 6$, $6 - 6 = 0$. Bring down 1.
- Tens: $1 \div 6$ is 0. Write 0. $0 \times 6 = 0$, $1 - 0 = 1$. Bring down 8 to make 18.
- Ones: $18 \div 6 = 3$. Write 3. $3 \times 6 = 18$, $18 - 18 = 0$.
- Check: $103 \times 6 = 618$.
Answer: $103$
Worked example: Starting with two digits
Find $1{,}575 \div 4$.
- 1 thousand is too small for 4 groups, so start with 15 hundreds: $15 \div 4 = 3$. $3 \times 4 = 12$, $15 - 12 = 3$. Bring down 7.
- Tens: $37 \div 4 = 9$. $9 \times 4 = 36$, $37 - 36 = 1$. Bring down 5.
- Ones: $15 \div 4 = 3$. $3 \times 4 = 12$, $15 - 12 = 3$. Nothing left to bring down.
- Check: $393 \times 4 + 3 = 1{,}575$.
Answer: $393$ R $3$
Common mistake
Skipping the 0: writing $618 \div 6 = 13$. Every place after the first one you divide needs a digit in the quotient. Multiply to check: $13 \times 6 = 78$, nowhere near 618.