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Partial quotients division, explained for parents
If your child's homework shows division as a list of subtractions with numbers down the side, that's the partial quotients method. Many US schools teach it in 4th and 5th grade, before or alongside standard long division.
The idea: take away easy chunks of the divisor (10 lots, 20 lots, 5 lots) until nothing is left, then add up how many lots you took. Children can use any chunks they're comfortable with, so it's forgiving while they learn.
Worked example: 456 ÷ 12
- Take away 20 twelves: 20 × 12 = 240, and 456 − 240 = 216.
- Take away 10 more twelves: 10 × 12 = 120, and 216 − 120 = 96.
- Take away 8 twelves: 8 × 12 = 96, and 96 − 96 = 0.
- Add the chunks: 20 + 10 + 8 = 38, so 456 ÷ 12 = 38. Check: 38 × 12 = 456.
6 practice problems
- 384 ÷ 16 = ?
- 672 ÷ 8 = ?
- 945 ÷ 15 = ?
- 1,092 ÷ 21 = ?
- 728 ÷ 13 = ?
- 500 ÷ 12 = ?
Show answers
- 384 ÷ 16 = 24
- 672 ÷ 8 = 84
- 945 ÷ 15 = 63
- 1,092 ÷ 21 = 52
- 728 ÷ 13 = 56
- 500 ÷ 12 = 41 R 8
Tips for parents
- Start with easy chunks: 10 times and 100 times the divisor.
- Bigger chunks mean fewer steps, but any chunk that fits is correct.
- If what's left is smaller than the divisor, that's the remainder.
Questions parents ask
Is partial quotients the same as long division?
It gives the same answer, but it's more flexible. Long division finds one digit at a time, while partial quotients lets your child take away any easy chunk. Many children later switch to standard long division.