Long Division Step by Step: An Easy Method (With Remainders)

Long division looks intimidating because there is a lot written on the page. But every long division problem, however big, repeats the same four small steps. Once a student can do those four steps reliably, the size of the number stops mattering.

The four steps: Divide, Multiply, Subtract, Bring down

• Divide: how many times does the divisor go into the current number?
• Multiply: multiply that answer by the divisor.
• Subtract: take the product away from the current number.
• Bring down: bring down the next digit and start again.

Many classrooms remember the order with a silly sentence such as "Does McDonald's Sell Burgers?" — D, M, S, B. Repeat the cycle until there are no digits left to bring down.

Worked example 1: 952 ÷ 4

• Divide: 4 goes into 9 two times. Write 2 above the 9.
• Multiply: 2 × 4 = 8. Write 8 under the 9.
• Subtract: 9 − 8 = 1.
• Bring down the 5 to make 15.
• Divide: 4 goes into 15 three times (4 × 3 = 12). Write 3 above the 5.
• Subtract: 15 − 12 = 3. Bring down the 2 to make 32.
• Divide: 4 goes into 32 exactly 8 times. 32 − 32 = 0.

So 952 ÷ 4 = 238. Check it by multiplying back: 238 × 4 = 952. ✓

Worked example 2: a remainder

Try 7,465 ÷ 6. Working through the same cycle gives 1,244 with 1 left over at the end, because 6 × 1,244 = 7,464 and 7,465 − 7,464 = 1. Write the answer as 1,244 R1.

Check every remainder: it must be smaller than the divisor. A remainder of 7 when dividing by 6 means another 6 would have fitted — the quotient digit was too small.

Worked example 3: a zero in the answer

In 812 ÷ 4, 4 goes into 8 twice. Bring down the 1: 4 does not go into 1, so write 0 in the quotient — this is the step students most often skip. Bring down the 2 to make 12, and 4 goes into 12 three times. The answer is 203, not 23.

Two-digit divisors

With a divisor like 24, the steps are identical, but the Divide step needs an estimate. For 1,872 ÷ 24, ask how many 24s are in 187. Round 24 to 25: 25 × 7 = 175, so try 7. Then 7 × 24 = 168 and 187 − 168 = 19. Bring down the 2 to make 192, and 24 × 8 = 192 exactly. The answer is 78.

If an estimate is too big, the product will be larger than the number you're subtracting from; if it's too small, the difference will be bigger than the divisor. Either way, adjust by one and try again.

The mistakes to watch for

• Forgetting a zero in the quotient when the divisor doesn't fit after bringing down a digit.
• Misaligned columns. Use squared paper so every digit sits in its own place-value column.
• Weak multiplication facts. Most long division errors are really times-table errors in the Multiply step. A few minutes of multiplication facts practice a day speeds everything up.
• Not checking. Multiplying the answer by the divisor (and adding any remainder) takes ten seconds and catches almost every slip.

When do students learn it?

Under the Common Core, students divide up to four-digit numbers by one-digit divisors in Grade 4 (4.NBT.B.6), move to two-digit divisors in Grade 5 (5.NBT.B.6) and are expected to be fluent with the standard algorithm in Grade 6 (6.NS.B.2).

Practice tip: do three or four problems a day rather than a page of twenty. Short, accurate practice builds the routine; long sessions build mistakes.