← Back to the Long Division worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Every problem has a worked solution with the final answer in bold and a multiplication check where useful. Compare each partial product and subtraction with your own work to find any slip.
Standards: 6.NS.B.2 · Level: Grade 6
Problem 1 Naming the Parts
Dividend 456, divisor 12, quotient 38. Check: 12 × 38 = 456.
Answer: dividend 456, divisor 12, quotient 38.
Problem 2 Estimating Quotients
(a) 612 ≈ 600 and 29 ≈ 30, so 600 ÷ 30 = 20.
(b) 4,185 ≈ 4,200 and 52 ≈ 50, so 4,200 ÷ 50 = 84.
Answer: (a) about 20; (b) about 84.
Problem 3 Two-Digit Divisor
98 ÷ 19 = 5 (95), remainder 3. Bring down 8 to make 38; 19 × 2 = 38.
Check: 19 × 52 = 988.
Answer: 52.
Problem 4 Another Two-Digit Divisor
113 ÷ 18 = 6 (108), remainder 5. Bring down 4 to make 54; 18 × 3 = 54.
Check: 18 × 63 = 1,134.
Answer: 63.
Problem 5 Missing Digits
75 ÷ 14 = 5, and 14 × 5 = 70. Subtract: 75 − 70 = 5, then bring down 6 to make 56.
Answer: 5, 0 and 5; the quotient is 54.
Problem 6 Quotient with Remainder
87 ÷ 26 = 3 (78), remainder 9. Bring down 5 to make 95; 26 × 3 = 78 and 95 − 78 = 17.
Check: 26 × 33 + 17 = 858 + 17 = 875.
Answer: 33 R 17.
Problem 7 Three-Digit Quotient
92 ÷ 34 = 2 (68), remainder 24. Bring down 8: 248 ÷ 34 = 7 (238), remainder 10. Bring down 2: 102 ÷ 34 = 3.
Check: 34 × 273 = 9,282.
Answer: 273.
Problem 8 Zero in the Quotient
63 ÷ 21 = 3 with remainder 0. Bring down 2: 21 does not fit into 2, so write 0. Bring down 7: 27 ÷ 21 = 1 remainder 6.
Check: 21 × 301 + 6 = 6,321 + 6 = 6,327.
Answer: 301 R 6.
Problem 9 Three-Digit Divisor
146 ÷ 144 = 1, remainder 2. Bring down 8: 28 does not fit, write 0. Bring down 8: 288 ÷ 144 = 2.
Check: 144 × 102 = 14,688.
Answer: 102.
Problem 10 Three-Digit Divisor with Remainder
523 ÷ 175 = 2 (350), remainder 173. Bring down 0: 1,730 ÷ 175 = 9 (1,575), remainder 155. Bring down 0: 1,550 ÷ 175 = 8 (1,400), remainder 150.
Check: 175 × 298 + 150 = 52,150 + 150 = 52,300.
Answer: 298 R 150.
Problem 11 Check the Claim
45 × 60 = 2,700, which is not 3,150, so the claim is wrong. 3,150 − 2,700 = 450 and 450 ÷ 45 = 10 more, so the quotient is 70. Check: 45 × 70 = 3,150.
Answer: 70.
Problem 12 Estimate and Divide
241 ÷ 35 = 6 (210), remainder 31. Bring down 5: 315 ÷ 35 = 9.
Check: 35 × 69 = 2,415. The estimate 70 is 1 more than 69.
Answer: 69.
Problem 13 Buses for a Field Trip
250 ÷ 48 = 5 R 10, since 48 × 5 = 240 and 250 − 240 = 10.
The 10 students left over still need a bus.
Answer: 6 buses.
Problem 14 Packs of Pencils
350 ÷ 12 = 29 R 2, because 12 × 29 = 348.
Answer: 29 full packs with 2 pencils left.
Problem 15 Cutting a Rope
(a) 275 ÷ 12 = 22 R 11, because 12 × 22 = 264.
(b) The remainder 11 is shared among 12: 22 1112.
Answer: (a) 22 full pieces with 11 feet left; (b) 22 1112.
Problem 16 Classroom Markers
Total markers: 36 × 24 = 864. Then 864 ÷ 32 = 27, since 32 × 27 = 864.
Answer: 27 markers.
Problem 17 Cookie Cartons
Boxes: 4,500 ÷ 18 = 250, since 18 × 250 = 4,500.
Cartons: 250 ÷ 12 = 20 R 10, and the 10 extra boxes need another carton.
Answer: 21 cartons.
Problem 18 Road Trip Days
(a) 1,596 ÷ 57 = 28, since 57 × 28 = 1,596.
(b) 28 ÷ 8 = 3 R 4, so after 3 days there are 4 hours left, which needs a fourth day.
Answer: (a) 28 hours; (b) 4 days.
Problem 19 Team Fundraiser
3,468 ÷ 17 = 204, since 17 × 204 = 3,468.
204 ÷ 12 = 17, since 12 × 17 = 204.
Answer: $204 per team, which buys 17 shirts.
Problem 20 Concert Rows
(a) 2,150 ÷ 38 = 56 R 22, since 38 × 56 = 2,128. The 22 extra guests need another row, so 57 rows.
(b) 38 − 22 = 16.
Answer: (a) 57 rows; (b) 16 empty seats.