Long division and checking remainders
Divide a multi-digit whole number and interpret what a remainder means in context.
Before you begin
- Multiplication facts
- Place value to thousands
Build the quotient one place at a time
Long division records repeated groups efficiently. Start with the leftmost part of the dividend that is at least as large as the divisor. Estimate how many groups fit, write that digit in the matching place of the quotient, multiply and subtract. Bring down the next digit and repeat. A zero in the quotient holds a place when no groups fit at that stage; skipping it changes the value.
Check and interpret a remainder
At the end, the remainder must be smaller than the divisor. Check by multiplying the quotient by the divisor and adding the remainder. The context decides what to do next: unused counters can remain, a measurement can continue into decimals, and vehicles needed for all passengers may require rounding up. A correct division calculation can still give a wrong practical answer if its remainder is ignored.
Worked example
Divide 1,764 by 14 without a calculator.
Show the worked solution
- 14 fits into 17 once. Subtract 14 and bring down 6 to make 36.
- 14 fits into 36 twice. Subtract 28 and bring down 4 to make 84.
- 14 fits into 84 six times. The quotient is 126; 14 × 126 = 1,764.
126.
Try it yourself
How many 24-seat minibuses are needed for 101 passengers?
Common mistakes
- Keep a zero when a quotient place has no whole groups.
- The remainder is not automatically a decimal digit.
What can you explain now?
Calculate 2,457 ÷ 12 and verify your result.
Compare with the explanation
204 remainder 9.
12 × 204 + 9 = 2,457. The zero in 204 is essential: after dividing 24, the next digit 5 is smaller than 12.
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗