Long Division Step by Step: A 4th and 5th Grade Walkthrough

What is long division?

Long division is a written method for dividing a larger number by a smaller one, one digit at a time. It is the standard arithmetic algorithm taught in U.S. 4th and 5th grade after students master single-digit division and multi-digit multiplication.

A long-division problem has three pieces:

• The dividend — the number being divided (the big number on the inside of the bracket).
• The divisor — the number you are dividing by (sits on the left of the bracket).
• The quotient — the answer you write on top, digit by digit.

If the dividend does not split evenly, the leftover amount is the remainder.

The four-step rhythm

Every long-division problem repeats the same four steps. Many teachers use the rhyme Divide, Multiply, Subtract, Bring Down — sometimes called DMSB or "Does McDonald's Sell Burgers?" to help students remember the order.

1. Divide. How many times does the divisor fit into the current piece of the dividend? Write that digit on top.
2. Multiply. Multiply the divisor by the digit you just wrote and write the product underneath.
3. Subtract. Subtract that product from the piece of the dividend above it. The result must be smaller than the divisor.
4. Bring down. Drag down the next digit of the dividend so you have a new piece to divide. Repeat from step 1.

When there are no more digits to bring down, you are done. Whatever is left after the last subtraction is the remainder.

Worked example 1: simple, no remainder

Compute $84 \div 4$ using long division.

   2 1
  ┌────
4 │ 8 4
   -8
   ──
    0 4
    -4
    ──
     0

Step by step:

1. Divide. $4$ goes into $8$ exactly $2$ times. Write $2$ on top above the $8$.
2. Multiply. $2 \times 4 = 8$. Write $8$ below the $8$.
3. Subtract. $8 - 8 = 0$.
4. Bring down the $4$. Now divide $4$ by $4$, which is $1$. Write $1$ on top above the $4$. Then $1 \times 4 = 4$, and $4 - 4 = 0$.

There are no more digits, and the remainder is $0$. The answer is $\mathbf{84 \div 4 = 21}$.

Worked example 2: with a remainder

Compute $97 \div 6$.

1. $6$ does not fit into $9$ that many times — only once. Write $1$ on top above the $9$.
2. $1 \times 6 = 6$. Subtract: $9 - 6 = 3$.
3. Bring down the $7$ to make $37$.
4. $6$ goes into $37$ exactly $6$ times. Write $6$ on top above the $7$.
5. $6 \times 6 = 36$. Subtract: $37 - 36 = 1$. No more digits to bring down.

The quotient is $16$ with a remainder of $1$. We write this as $97 \div 6 = 16 \text{ R } 1$, or as the mixed number $16\dfrac{1}{6}$.

Worked example 3: a longer dividend

Compute $725 \div 5$.

1. $5$ goes into $7$ once. Write $1$ on top. $1 \times 5 = 5$. Subtract: $7 - 5 = 2$.
2. Bring down the $2$ to make $22$. $5$ goes into $22$ four times. Write $4$ on top. $4 \times 5 = 20$. Subtract: $22 - 20 = 2$.
3. Bring down the $5$ to make $25$. $5$ goes into $25$ exactly $5$ times. Write $5$ on top. $5 \times 5 = 25$. Subtract: $25 - 25 = 0$.

The quotient is $\mathbf{145}$, no remainder.

Worked example 4: the "doesn't fit" digit

Compute $312 \div 4$.

1. $4$ goes into $3$ zero times — $4$ is bigger than $3$. Skip it: do not write a $0$ on top yet, but read the first two digits as $31$.
2. $4$ goes into $31$ seven times. Write $7$ on top above the $1$. $7 \times 4 = 28$. Subtract: $31 - 28 = 3$.
3. Bring down the $2$ to make $32$. $4$ goes into $32$ eight times. Write $8$ on top. $8 \times 4 = 32$. Subtract: $32 - 32 = 0$.

The quotient is $\mathbf{78}$, no remainder. Notice the answer has only two digits because we skipped the leading position where the divisor did not fit.

Worked example 5: a zero in the middle

Compute $604 \div 3$.

1. $3$ goes into $6$ exactly $2$ times. Write $2$ on top. $2 \times 3 = 6$. Subtract: $6 - 6 = 0$.
2. Bring down the $0$. Now divide $0$ by $3$ — that's $0$ times. Write $0$ on top. (This zero is important; without it the quotient would be wrong.) $0 \times 3 = 0$. Subtract: $0 - 0 = 0$.
3. Bring down the $4$. $3$ goes into $4$ once. Write $1$ on top. $1 \times 3 = 3$. Subtract: $4 - 3 = 1$.

The quotient is $\mathbf{201}$ with a remainder of $1$. The middle $0$ is exactly what makes the answer line up correctly.

Three tips that prevent most mistakes

• Line up your columns. Sloppy spacing is the number-one source of long-division errors. Use grid paper or draw your own tick marks.
• Always check the subtraction is smaller than the divisor. If you got a remainder of $5$ when dividing by $4$, your "Divide" step picked too small a digit — you can fit one more.
• Estimate first. Before starting, ask "About how big should the quotient be?" $725 \div 5$ should be around $700 \div 5 = 140$, so an answer of $145$ feels right; an answer of $14$ or $1450$ would tell you something went wrong.

Common mistakes

• Dropping the "skip" zero. When the divisor does not fit and you bring down the next digit, write a $0$ in the corresponding spot of the quotient if it appears in the middle of the answer.
• Stopping before bringing down every digit. The quotient must have one digit (or a skipped zero) for every digit in the dividend after the place where the divisor first fits.
• Forgetting the remainder. If the final subtraction is not zero, that leftover number is the remainder — write it as "R 3" or as a fraction.