Long Division with Partial Quotients and Area Models
Print 4th grade long division worksheets: divide 3- and 4-digit numbers by 1-digit numbers with area models and partial quotients. 12 versions with keys.
Worksheet version 1 of 12. The answer key matches the current version.
Divide in chunks: take away chunks of the divisor, biggest place first (thousands or hundreds, then tens, then ones). Add the chunks to get the quotient, write the remainder, then check by multiplying back. The remainder is 0 when nothing is left.
A. Fill in each area model. Write the partial quotient above each box and the amount it takes away inside.
1) 8,528 ÷ 3
Quotient: ______ R ____
Check: _____ × ___ + ___ = _______
2) 357 ÷ 8
Quotient: ______ R ____
Check: _____ × ___ + ___ = _______
3) 644 ÷ 7
Quotient: ______ R ____
Check: _____ × ___ + ___ = _______
B. Use the ladder. Take away chunks of the divisor until less than one divisor is left.
4) 8,848 ÷ 4
| Left to divide | Take away | Partial quotient |
|---|---|---|
| 8,848 | ||
| Left: ____ | Total: _____ |
Quotient: ______ R ____
Check: _____ × ___ + ___ = _______
5) 2,286 ÷ 9
| Left to divide | Take away | Partial quotient |
|---|---|---|
| 2,286 | ||
| Left: ____ | Total: _____ |
Quotient: ______ R ____
Check: _____ × ___ + ___ = _______
6) 953 ÷ 6
| Left to divide | Take away | Partial quotient |
|---|---|---|
| 953 | ||
| Left: ____ | Total: _____ |
Quotient: ______ R ____
Check: _____ × ___ + ___ = _______
About this worksheet
Partial quotients is a way to divide big numbers one friendly chunk at a time. To work out 1,407 ÷ 6, ask how many hundreds of sixes fit: 200 sixes make 1,200, which leaves 207. Then 30 sixes make 180, which leaves 27, and 4 sixes make 24, which leaves 3. The chunks add up to the quotient, 234, and the 3 that is left is the remainder. It is the same thinking as the standard long division algorithm, with every step written out by place value.
Part A draws three area models: the divisor is the height of the rectangle, the dividend is its area, and each box is one chunk. Students write each box's width (the partial quotient) above it and its area inside. Part B uses a partial-quotient ladder with columns for what is left, what to take away and the chunk. Every version mixes three-digit and four-digit dividends with divisors from 2 to 9, and half of the six problems have a remainder. Each problem ends with a check: quotient × divisor + remainder should give the dividend back. The answer key shows one chunk for each place of the quotient; students who take different chunks (like 100 twice instead of 200) are still right if the total matches.
Practice aligned to CCSS 4.NBT.B.6.
Before this: division with remainders within the times tables and four-digit by one-digit multiplication, which is how each answer is checked. Next: multi-step word problems, where the remainder has to be interpreted. More practice: division worksheets and 4th grade math worksheets.
Related Math Worksheets
Free printable 3rd grade division fact fluency worksheet: basic division facts within 100 with no remainders, the inverse of the times tables kids already know.
Free 4th grade division with remainders worksheet: practice quotients and remainders with facts within 100 (CCSS 4.NBT.B.6).
Print 4th grade multi-step word problems: practice all four operations, write equations with variables, and interpret division remainders with answer keys.