Partial Quotient Division Worksheets With the Side Column Drawn

Division by easy chunks, with a side column to add up and an answer key.

Sheet type

Problems

Answer key

6 problems. 3-digit ÷ 1-digit in chunks, no remainder. Sheet 7I6XDS, with its answer key.

3-digit ÷ 1-digit in chunks, no remainder

Name Date Score / 6

Divide with partial quotients: take away easy multiples of the divisor, note each one at the side, then add them up.

Sheet 7I6XDS · Made at homeroomtools.com

Answer key. 3-digit ÷ 1-digit in chunks, no remainder

1.181
2.333
3.198
4.133
5.111
6.215

Sheet 7I6XDS · Made at homeroomtools.com

Next step Try the same sizes in long division See the same chunks drawn as boxes

How it works

Each bracket on these partial quotient division worksheets has a side column for the chunks. The page opens on 3-digit ÷ 1-digit, such as 738 ÷ 6 = 123; the largest sheet reaches 5,000 ÷ 48 = 104 R 8.

Read the full guide

How partial quotients works

Pupils take away easy multiples of the divisor and keep a tally of groups down the side. For 738 ÷ 6, take 600 and write 100 in the side column. Take 120 from the 138 left and write 20. Take the last 18 and write 3. The column adds up to 100 + 20 + 3 = 123. Smaller chunks reach the same answer in more lines.

Chunking, hangman and other names

British primary schools call the method chunking. With a line between the working and the partial quotients it is also called the hangman method. England's curriculum sets out its long division example, 432 ÷ 15, in chunks: it subtracts 300 and 120 and notes 15 × 20 and 15 × 8 beside them.

Print Easy multiples of the divisor: × 2, × 5, × 10, × 20 first: those products are the chunks.
A pupil who takes 10 groups again and again is ready for Fewest chunks: hundreds, tens, ones.
Repeated subtraction, one group at a time shows what the side column counts: groups of the divisor.

Questions and answers

What grade is partial quotients division?

The number sizes are grades 4 and 5. Common Core 4.NBT.6 asks for quotients and remainders with up to 4-digit dividends and 1-digit divisors, using strategies based on place value. 5.NBT.6 moves to 2-digit divisors. Neither names a method; partial quotients is one such strategy.

How do you do partial quotients with a remainder?

Keep taking chunks until what is left is smaller than the divisor. For 95 ÷ 4, take 40, 40 and 12. The side column adds up to 23 and 3 is left: 23 R 3. Check: 23 × 4 + 3 = 95.

Which chunks should pupils take away?

Any multiple of the divisor they are sure of. Times 10, 5 and 2 are the usual picks: for 945 ÷ 27 that makes 270, 135 and 54. The key heads its chunks One way: any set adding up to the quotient is right.

Is partial quotients the same as long division?

Long division takes the largest chunk at each place, so 952 ÷ 7 goes 700, 210, 42. Partial quotients allows any. The side column makes a lost zero easy to spot: No tens chunk: quotients like 206 has 824 ÷ 4 = 200 + 6.

All 16 sheet types

First chunks and warm-ups 5

2-digit ÷ 1-digit, a tens chunk then the rest 84 ÷ 6 = 14: take 60, which is 10 sixes, then 24, which is 4 sixes, and 10 + 4 = 14. Every problem needs exactly one chunk of 10 groups, so pupils learn the opening move before the numbers grow.
2-digit ÷ 1-digit, something left over 95 ÷ 4 = 23 R 3: take 40, another 40, then 12, and 3 is left. Pupils stop when the number left is smaller than the divisor, because no more whole groups fit.
Easy multiples of the divisor: × 2, × 5, × 10, × 20 20 quick products such as 14 × 5 = 70 and 14 × 20 = 280. These are the chunks pupils will take away, so a minute on them first means nobody stalls halfway down a division.
Facts for the last chunk: ÷ 6, 7, 8 and 9 40 division facts written across the page, such as 56 ÷ 7 = 8. The last chunk of every problem is a single fact, and the 6 to 9 tables are where it goes wrong. This is the one sheet here built from single facts.
Repeated subtraction, one group at a time 35 ÷ 7 = 5 by taking away 7 five times and writing a 1 in the side column each time. It is the slowest way to divide, and it shows pupils what the side column counts: groups of the divisor.

Show all 16 sheet types (11 more)

1-digit divisors 5

3-digit ÷ 1-digit in chunks, no remainder 738 ÷ 6 = 123: take 600 (100 sixes), 120 (20 sixes) and 18 (3 sixes), then add the side column, 100 + 20 + 3 = 123. The page opens on this sheet. A pupil who takes 300 twice still gets 123.
3-digit ÷ 1-digit in chunks, with a remainder 527 ÷ 3 = 175 R 2: take 300, 150, 60 and 15, which are 100, 50, 20 and 5 threes, and 2 is left. Four chunks is a normal count here. The key shows one way that works, and other chunks are right if they add up to the same quotient.
4-digit ÷ 1-digit in chunks, no remainder 4,368 ÷ 7 = 624: take 4,200 (600 sevens), 140 (20 sevens) and 28 (4 sevens). The first chunk comes from a fact with zeros added, since 6 × 7 = 42 gives 600 × 7 = 4,200.
4-digit ÷ 1-digit in chunks, with a remainder 5,219 ÷ 8 = 652 R 3: take 4,800, then 400, then 16, and 3 is left. This is the largest size Common Core 4.NBT.6 asks for: up to 4-digit dividends, 1-digit divisors, quotients and remainders.
No tens chunk: quotients like 206 824 ÷ 4 = 206: take 800 (200 fours), then 24 (6 fours). No chunk of tens is needed, and adding 200 + 6 puts the 0 in place by itself. In the bracket method the same problem is where pupils write 26.

2-digit divisors 5

3-digit ÷ 2-digit in chunks, no remainder 945 ÷ 27 = 35: take 540 (20 groups), 270 (10 groups) and 135 (5 groups). Doubling and halving do the work: 270 doubled is 540, and half of 270 is 135. No one has to guess how many 27s fit in 94.
3-digit ÷ 2-digit in chunks, with a remainder 432 ÷ 15 = 28 R 12: take 300 (20 fifteens), then 120 (8 fifteens), and 12 is left. England's curriculum prints this same working as its long division example, with 15 × 20 and 15 × 8 noted beside the subtractions.
3-digit ÷ 2-digit, quotients under 20 156 ÷ 12 = 13: take 120, which is 10 twelves, then 36, which is 3 twelves. Ten groups of a 2-digit number is the easiest chunk there is, so this is the first sheet to use with a 2-digit divisor.
4-digit ÷ 2-digit in chunks, no remainder 2,944 ÷ 23 = 128: take 2,300 (100 groups), 460 (20 groups) and 184 (8 groups). The last chunk is the hard one. A pupil unsure of 23 × 8 can take 92 twice, which is 4 groups and 4 more.
4-digit ÷ 2-digit in chunks, with a remainder 5,000 ÷ 48 = 104 R 8: take 4,800 (100 groups), then 192 (4 groups), and 8 is left. Two chunks finish a problem that takes three rounds of steps in the bracket, one of them a 0 that is easy to forget.

Toward long division, and review 1

Fewest chunks: hundreds, tens, ones 952 ÷ 7 = 136 in exactly three chunks: 700, then 210, then 42. Each chunk is the largest number of hundreds, tens or ones that fits. Those three numbers are the ones long division subtracts, so this sheet is the bridge to it.

How this list was compiled: The sheet types and worked sums were written for this page, except 432 ÷ 15, the long division example in England's national curriculum, whose own working subtracts 300 and then 120. The method and its names (chunking, partial quotients, hangman) were checked on 2026-09-19 and again on 2026-09-20 against https://en.wikipedia.org/wiki/Chunking_(division). Number sizes and standard numbers were checked on 2026-09-19 against the Common Core State Standards for Mathematics (https://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf), the Texas Essential Knowledge and Skills for Mathematics (https://tea.texas.gov/sites/default/files/ch111a.pdf) and the national curriculum in England (https://assets.publishing.service.gov.uk/media/5a7da548ed915d2ac884cb07/PRIMARY_national_curriculum_-_Mathematics_220714.pdf, Open Government Licence). None of the three names partial quotients or chunking. Licence: own work