Division

Long Division

3-Digit ÷ 1-Digit

Divide 936 ÷ 9. The second quotient digit is 0 — 9 doesn't divide into 3, so you write 0 and bring down the next digit. This shows what to do when the divisor is bigger than the working number.

Example

Divide 936 by 9 using the long-division galley.

highlighted = computed this step

Step 1 — Set up

Set up the long-division galley.

x□□□9936\begin{array}{r|rrr}\phantom{x}&\square&\square&\square\\\hline\\9&9&3&6\end{array}
Set up 936 divided by 9.99dividend3dividend6dividend□quotient□quotient□quotientdividenot yetmultiplynot yetsubtractnot yetbring downnot yetdividenot yetmultiplynot yetsubtractnot yetbring downnot yetdividenot yetmultiplynot yetsubtractnot yetcheck: 9 x 104 + 0 = 936

Step 2 — Write quotient digit

9 ÷ 9 = 1, write 1.

x1□□9936\begin{array}{r|rrr}\phantom{x}&\hl{1}&\square&\square\\\hline\\9&9&3&6\end{array}
Use the first digit: 9 ÷ 9 = 1.99dividend3dividend6dividend1quotient□quotient□quotientdivide9 ÷ 9 = 1multiplynot yetsubtractnot yetbring downnot yetdividenot yetmultiplynot yetsubtractnot yetbring downnot yetdividenot yetmultiplynot yetsubtractnot yetcheck: 9 x 104 + 0 = 936

Step 3 — Multiply back

Multiply back: 1 x 9 = 9.

x1□□9936x9xx\begin{array}{r|rrr}\phantom{x}&1&\square&\square\\\hline\\9&9&3&6\\\phantom{x}&\hl{9}&\phantom{x}&\phantom{x}\end{array}
Multiply back: 1 x 9 = 9.99dividend3dividend6dividend1quotient□quotient□quotient9divide9 ÷ 9 = 1multiply1 x 9 = 9subtractnot yetbring downnot yetdividenot yetmultiplynot yetsubtractnot yetbring downnot yetdividenot yetmultiplynot yetsubtractnot yetcheck: 9 x 104 + 0 = 936

Step 4 — Subtract

Subtract: 9 - 9 = 0.

x1□□9936x9xxx0xx\begin{array}{r|rrr}\phantom{x}&1&\square&\square\\\hline\\9&9&3&6\\\phantom{x}&9&\phantom{x}&\phantom{x}\\\phantom{x}&\hl{0}&\phantom{x}&\phantom{x}\end{array}
Subtract: 9 - 9 = 0.99dividend3dividend6dividend1quotient□quotient□quotient90divide9 ÷ 9 = 1multiply1 x 9 = 9subtract9 - 9 = 0bring downnot yetdividenot yetmultiplynot yetsubtractnot yetbring downnot yetdividenot yetmultiplynot yetsubtractnot yetcheck: 9 x 104 + 0 = 936

Step 5 — Bring down

Bring down the 3; the new working number is 3.

x1□□9936x9xxx0xx\begin{array}{r|rrr}\phantom{x}&1&\square&\square\\\hline\\9&9&\hl{3}&6\\\phantom{x}&9&\phantom{x}&\phantom{x}\\\phantom{x}&0&\phantom{x}&\phantom{x}\end{array}
Bring down 3: 0 and 3 make 3.99dividend3dividend6dividend1quotient□quotient□quotient90bring down 33divide9 ÷ 9 = 1multiply1 x 9 = 9subtract9 - 9 = 0bring down0 with 3 makes 3dividenot yetmultiplynot yetsubtractnot yetbring downnot yetdividenot yetmultiplynot yetsubtractnot yetcheck: 9 x 104 + 0 = 936

Step 6 — Write quotient digit

3 ÷ 9 = 0, write 0.

x10□9936x9xxx0xx\begin{array}{r|rrr}\phantom{x}&1&\hl{0}&\square\\\hline\\9&9&3&6\\\phantom{x}&9&\phantom{x}&\phantom{x}\\\phantom{x}&0&\phantom{x}&\phantom{x}\end{array}
3 ÷ 9 = 0; write 0 to hold the tens place.99dividend3dividend6dividend1quotient0quotient□quotient90bring down 33divide9 ÷ 9 = 1multiply1 x 9 = 9subtract9 - 9 = 0bring down0 with 3 makes 3divide3 ÷ 9 = 0 (write 0)multiplynot yetsubtractnot yetbring downnot yetdividenot yetmultiplynot yetsubtractnot yetcheck: 9 x 104 + 0 = 936

Step 7 — Multiply back

Multiply back: 0 x 9 = 0.

x10□9936x9xxx0xxxx0x\begin{array}{r|rrr}\phantom{x}&1&0&\square\\\hline\\9&9&3&6\\\phantom{x}&9&\phantom{x}&\phantom{x}\\\phantom{x}&0&\phantom{x}&\phantom{x}\\\phantom{x}&\phantom{x}&\hl{0}&\phantom{x}\end{array}
Multiply back: 0 x 9 = 0.99dividend3dividend6dividend1quotient0quotient□quotient900bring down 33divide9 ÷ 9 = 1multiply1 x 9 = 9subtract9 - 9 = 0bring down0 with 3 makes 3divide3 ÷ 9 = 0 (write 0)multiply0 x 9 = 0subtractnot yetbring downnot yetdividenot yetmultiplynot yetsubtractnot yetcheck: 9 x 104 + 0 = 936

Step 8 — Subtract

Subtract: 3 - 0 = 3.

x10□9936x9xxx0xxxx0xxx3x\begin{array}{r|rrr}\phantom{x}&1&0&\square\\\hline\\9&9&3&6\\\phantom{x}&9&\phantom{x}&\phantom{x}\\\phantom{x}&0&\phantom{x}&\phantom{x}\\\phantom{x}&\phantom{x}&0&\phantom{x}\\\phantom{x}&\phantom{x}&\hl{3}&\phantom{x}\end{array}
Subtract: 3 - 0 = 3.99dividend3dividend6dividend1quotient0quotient□quotient9003bring down 33divide9 ÷ 9 = 1multiply1 x 9 = 9subtract9 - 9 = 0bring down0 with 3 makes 3divide3 ÷ 9 = 0 (write 0)multiply0 x 9 = 0subtract3 - 0 = 3bring downnot yetdividenot yetmultiplynot yetsubtractnot yetcheck: 9 x 104 + 0 = 936

Step 9 — Bring down

Bring down the 6; the new working number is 36.

x10□9936x9xxx0xxxx0xxx3x\begin{array}{r|rrr}\phantom{x}&1&0&\square\\\hline\\9&9&3&\hl{6}\\\phantom{x}&9&\phantom{x}&\phantom{x}\\\phantom{x}&0&\phantom{x}&\phantom{x}\\\phantom{x}&\phantom{x}&0&\phantom{x}\\\phantom{x}&\phantom{x}&3&\phantom{x}\end{array}
Bring down 6: 3 and 6 make 36.99dividend3dividend6dividend1quotient0quotient□quotient9003bring down 33bring down 636divide9 ÷ 9 = 1multiply1 x 9 = 9subtract9 - 9 = 0bring down0 with 3 makes 3divide3 ÷ 9 = 0 (write 0)multiply0 x 9 = 0subtract3 - 0 = 3bring down3 with 6 makes 36dividenot yetmultiplynot yetsubtractnot yetcheck: 9 x 104 + 0 = 936

Step 10 — Write quotient digit

36 ÷ 9 = 4, write 4.

x1049936x9xxx0xxxx0xxx3x\begin{array}{r|rrr}\phantom{x}&1&0&\hl{4}\\\hline\\9&9&3&6\\\phantom{x}&9&\phantom{x}&\phantom{x}\\\phantom{x}&0&\phantom{x}&\phantom{x}\\\phantom{x}&\phantom{x}&0&\phantom{x}\\\phantom{x}&\phantom{x}&3&\phantom{x}\end{array}
Now 36 ÷ 9 = 4.99dividend3dividend6dividend1quotient0quotient4quotient9003bring down 33bring down 636divide9 ÷ 9 = 1multiply1 x 9 = 9subtract9 - 9 = 0bring down0 with 3 makes 3divide3 ÷ 9 = 0 (write 0)multiply0 x 9 = 0subtract3 - 0 = 3bring down3 with 6 makes 36divide36 ÷ 9 = 4multiplynot yetsubtractnot yetcheck: 9 x 104 + 0 = 936

Step 11 — Multiply back

Multiply back: 4 x 9 = 36.

x1049936x9xxx0xxxx0xxx3xxx36\begin{array}{r|rrr}\phantom{x}&1&0&4\\\hline\\9&9&3&6\\\phantom{x}&9&\phantom{x}&\phantom{x}\\\phantom{x}&0&\phantom{x}&\phantom{x}\\\phantom{x}&\phantom{x}&0&\phantom{x}\\\phantom{x}&\phantom{x}&3&\phantom{x}\\\phantom{x}&\phantom{x}&\hl{3}&\hl{6}\end{array}
Multiply back: 4 x 9 = 36.99dividend3dividend6dividend1quotient0quotient4quotient900336bring down 33bring down 636divide9 ÷ 9 = 1multiply1 x 9 = 9subtract9 - 9 = 0bring down0 with 3 makes 3divide3 ÷ 9 = 0 (write 0)multiply0 x 9 = 0subtract3 - 0 = 3bring down3 with 6 makes 36divide36 ÷ 9 = 4multiply4 x 9 = 36subtractnot yetcheck: 9 x 104 + 0 = 936

Step 12 — Subtract

Subtract: 36 - 36 = 0.

x1049936x9xxx0xxxx0xxx3xxx36xxx0\begin{array}{r|rrr}\phantom{x}&1&0&4\\\hline\\9&9&3&6\\\phantom{x}&9&\phantom{x}&\phantom{x}\\\phantom{x}&0&\phantom{x}&\phantom{x}\\\phantom{x}&\phantom{x}&0&\phantom{x}\\\phantom{x}&\phantom{x}&3&\phantom{x}\\\phantom{x}&\phantom{x}&3&6\\\phantom{x}&\phantom{x}&\phantom{x}&\hl{0}\end{array}
Subtract: 36 - 36 = 0.99dividend3dividend6dividend1quotient0quotient4quotient9003360bring down 33bring down 636divide9 ÷ 9 = 1multiply1 x 9 = 9subtract9 - 9 = 0bring down0 with 3 makes 3divide3 ÷ 9 = 0 (write 0)multiply0 x 9 = 0subtract3 - 0 = 3bring down3 with 6 makes 36divide36 ÷ 9 = 4multiply4 x 9 = 36subtract36 - 36 = 0check: 9 x 104 + 0 = 936

Step 13 — Result

Read the quotient 104 with remainder 0.

x1049936x9xxx0xxxx0xxx3xxx36xxx0\begin{array}{r|rrr}\phantom{x}&1&0&4\\\hline\\9&9&3&6\\\phantom{x}&9&\phantom{x}&\phantom{x}\\\phantom{x}&0&\phantom{x}&\phantom{x}\\\phantom{x}&\phantom{x}&0&\phantom{x}\\\phantom{x}&\phantom{x}&3&\phantom{x}\\\phantom{x}&\phantom{x}&3&6\\\phantom{x}&\phantom{x}&\phantom{x}&0\end{array}
Check: 9 x 104 + 0 = 936.99dividend3dividend6dividend1quotient0quotient4quotient9003360bring down 33bring down 636divide9 ÷ 9 = 1multiply1 x 9 = 9subtract9 - 9 = 0bring down0 with 3 makes 3divide3 ÷ 9 = 0 (write 0)multiply0 x 9 = 0subtract3 - 0 = 3bring down3 with 6 makes 36divide36 ÷ 9 = 4multiply4 x 9 = 36subtract36 - 36 = 0check: 9 x 104 + 0 = 936
zero-quotient-digit When the divisor is larger than the current working number, the quotient digit for that position is 0. You still multiply (0 × d = 0), subtract, and bring down the next digit — never skip a position.