Key takeaway: Long division is a step-by-step written method for dividing multi-digit numbers by repeating divide, multiply, subtract and bring down, one digit of the dividend at a time.
Grade 66.NS.B.2Numbers and Operations
Definition of Long Division
Long division splits a big dividend into equal groups, one place value at a time. You work from the left, find how many times the divisor fits into the digits so far, and record that digit in the quotient.
After each digit you multiply back, subtract to get the remainder, and bring down the next digit. The cycle repeats until every digit has been used. A final remainder of 0 means the divisor goes in evenly; otherwise you can continue with decimals.
Formula and notation
The divisor sits outside the bracket, the dividend inside, and the quotient above:
\[\text{dividend} = \text{divisor} \times \text{quotient} + \text{remainder}\]
Use this to check an answer: multiply the quotient by the divisor, add the remainder, and you should recover the dividend.
Key facts
- Every cycle has four moves: divide, multiply, subtract, bring down.
- Each remainder must be smaller than the divisor, or the quotient digit was too small.
- In long division, a zero goes in the quotient whenever the divisor does not fit into the current digits.
- Long division also handles decimals: add a decimal point and zeros, then keep going.
Long Division example
A school sold 4,368 raffle tickets in 12 equal bundles. How many tickets were in each bundle?
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\(12\) does not go into 4, so use 43: \(12 \times 3 = 36\), and \(43 – 36 = 7\).
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Bring down 6 to make 76: \(12 \times 6 = 72\), and \(76 – 72 = 4\).
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Bring down 8 to make 48: \(12 \times 4 = 48\), and \(48 – 48 = 0\).
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Check: \(12 \times 364 = 4{,}368\).
Each bundle held 364 tickets.
Common mistake
Watch out
Omar divides \(5{,}412 : 6\) and writes the quotient as 92.
Why it is wrong
After \(54 : 6 = 9\), the next digit is 1, and 6 does not fit into 1. That column needs a 0 in the quotient before bringing down the 2: \(12 : 6 = 2\). The quotient is 902, and \(6 \times 902 = 5{,}412\).
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Numbers and Operations