How to Do Long Division

• Dividend (591): the number being divided. It goes inside the bracket.
• Divisor (7): the number you divide by. It goes outside, on the left.
• Quotient (84): the answer. It's written on top, one digit at a time.
• Remainder (3): what's left over when the divisor no longer fits.

Long division is the same four steps, repeated once for every digit of the dividend:

1. Divide: how many whole times does the divisor fit into the number you're looking at? Write that digit on top.
2. Multiply: multiply that digit by the divisor and write the result underneath.
3. Subtract: subtract to find what's left. It must be smaller than the divisor.
4. Bring down: bring the next digit of the dividend down beside it.

Many classes remember the order as "Does McDonald's Sell Burgers?": Divide, Multiply, Subtract, Bring down. When there's nothing left to bring down, whatever remains is the remainder.

Work out 591 ÷ 7.

1. 7 doesn't go into 5, so look at the first two digits: 59.
2. Divide: 7 goes into 59 8 times (7 × 9 = 63 is too much). Write 8 above the 9.
3. Multiply 8 × 7 = 56 and subtract: 59 − 56 = 3.
4. Bring down the 1 to make 31. 7 goes into 31 4 times; 4 × 7 = 28, and 31 − 28 = 3.
5. Nothing is left to bring down, so the answer is 84 R 3.

Check it: 84 × 7 + 3 = 588 + 3 = 591 ✓

Work out 7,825 ÷ 25. The steps are the same; the hard part is the divide step, because the 25 times table is less familiar. Two tricks help:

• Write out a few multiples first: 25, 50, 75, 100. Now each divide step is a lookup.
• Estimate with rounding: for a divisor like 32, think "about 30". If your guess is too big, the multiply step will be larger than the number; go down by 1.

25 goes into 78 three times (75), leaving 3. Bring down the 2: 25 goes into 32 once, leaving 7. Bring down the 5: 25 goes into 75 three times exactly. The answer is 313 with no remainder.

Every digit you bring down must put a digit on top, even when the divisor doesn't fit. In 1,248 ÷ 12, after 12 ÷ 12 = 1 you bring down the 4, and 12 can't go into 4. Write 0 on top, then bring down the 8 to make 48.

Skipping that zero gives 14, which is ten times too small. A quick estimate (1,200 ÷ 12 = 100) shows the answer must have three digits.

Instead of stopping with a remainder, you can keep going. Put a decimal point after the dividend and directly above it in the answer, then bring down zeros.

22 ÷ 8 = 2 with 6 left. Bring down a 0: 60 ÷ 8 = 7 with 4 left. Bring down another 0: 40 ÷ 8 = 5 exactly. The answer is 2.75.

Sometimes the remainders never reach 0. In 10 ÷ 3 the remainder is 1 every time, so the answer is 3.333… forever. Once a remainder repeats, the digits repeat too, and you can write a bar over them: 3.3.

Long division needs a whole-number divisor. In 4.5 ÷ 0.15, move the decimal point in 0.15 two places right to get 15, and move the point in 4.5 two places too, adding a zero: 450. Both numbers were multiplied by 100, so the answer is the same.

If only the dividend has a decimal point, there's nothing to move. Divide as normal and put the answer's decimal point straight above the dividend's.

• Leaving out a zero when the divisor doesn't fit (14 instead of 104).
• A remainder as big as the divisor: if you subtract and get 7 or more when dividing by 7, the digit on top was too small.
• Misaligned columns: write each quotient digit directly above the last digit you brought down. Squared paper helps.
• Treating the remainder as decimals: 84 R 3 is 84 3/7 (about 84.43), not 84.3.
• Moving only one decimal point when the divisor is a decimal. Always move both by the same number of places.

Work these out on paper, then check your working with the Long Division Calculator.

1. 852 ÷ 6
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   142, since 142 × 6 = 852
2. 917 ÷ 4
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   229 R 1, since 229 × 4 + 1 = 917
3. 2,436 ÷ 12
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   203. 12 doesn't go into the 3 you bring down, so the middle digit is 0.
4. 6,750 ÷ 25
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   270. The last 0 brought down gives a 0 on top.
5. 1,000 ÷ 7
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   142 R 6, since 142 × 7 + 6 = 1,000
6. 15 ÷ 4, as a decimal
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   3.75. 15 ÷ 4 = 3 R 3, then 30 ÷ 4 = 7 R 2, then 20 ÷ 4 = 5.
7. 2 ÷ 3, as a decimal
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   0.666…, written 0.6. The remainder is 2 every time.
8. 7.2 ÷ 0.08
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   90. Move both points two places: 720 ÷ 8 = 90.