Kid Einsteins · Class 7 · Long Division · Grades 3–4 · NYC Math Class
Long Division with Three-Digit Dividends — 25 Practice Questions with Theory & Hidden Answers (Kid Einsteins Class 7)
This is Class 7 of the SOMATH Kid Einsteins multiplication & division arc — the class where students go from “I know my division facts” (that was Class 6) to “I can divide any three-digit number by a one-digit divisor.” This is the class where long division becomes real. We introduce the four-step DMSB cycle (Divide, Multiply, Subtract, Bring down), work through three fully solved examples together, then hand students 25 practice questions with hidden step-by-step answers and 5 challenge word problems.
What’s in this class
- What is long division?
- The DMSB cycle — the four-step long-division loop
- Example 1 — 672 ÷ 4 (no remainder)
- Example 2 — 754 ÷ 6 (with a remainder)
- Example 3 — 305 ÷ 5 (zero in the middle of the quotient)
- How to check every division answer
- 25 practice questions with hidden answers
- 5 challenge word problems
- Answer key table
- FAQ
1. What is long division?
In Class 6 we learned that division is the inverse of multiplication — if you know 6 × 7 = 42, then you also know 42 ÷ 6 = 7 and 42 ÷ 7 = 6. But division facts alone only get you so far. What happens when the number you’re dividing is bigger than any fact you memorized — something like 672 ÷ 4 or 856 ÷ 7?
That’s what long division is for. Long division is a step-by-step procedure that lets you divide any number by another number, digit by digit, using only the multiplication facts you already know.
The parts of a division problem
Every division problem has three parts (and often a fourth):
- Dividend — the number being divided (goes inside the long-division bracket)
- Divisor — the number you’re dividing by (goes outside, to the left of the bracket)
- Quotient — the answer (goes on top of the bracket)
- Remainder — what’s left over when the divisor doesn’t divide evenly (written as R next to the quotient)
Example: in 754 ÷ 6 = 125 R 4, the dividend is 754, the divisor is 6, the quotient is 125, and the remainder is 4.
2. The DMSB cycle
Divide, Multiply, Subtract, Bring down
Long division is a loop of four steps that you repeat, digit by digit, from left to right across the dividend:
- D — Divide. Look at the current chunk of the dividend. How many times does the divisor fit into it? Write that answer above the dividend.
- M — Multiply. Multiply your answer digit by the divisor. Write the product under the chunk.
- S — Subtract. Subtract the product from the chunk above it.
- B — Bring down. Bring down the next digit of the dividend next to what’s left. This is the new chunk. Go back to step 1.
Repeat until every digit of the dividend has been used. Whatever is left after the last subtraction is the remainder (or zero if it divides evenly).
Some teachers use a memory phrase for the order: “Dad, Mom, Sister, Brother” or “Does McDonald’s Sell Burgers?” Whatever helps students remember: divide, multiply, subtract, bring down.
3. Example 1 — 672 ÷ 4 (no remainder)
Set it up. The dividend 672 goes inside the bracket, the divisor 4 outside:
Round 1 — look at the 6 (hundreds digit).
- D: How many times does 4 go into 6? Answer: 1 (since 4 × 1 = 4 and 4 × 2 = 8 is too big). Write 1 above the 6.
- M: 1 × 4 = 4. Write 4 under the 6.
- S: 6 − 4 = 2. Write 2.
- B: Bring down the next digit (7). New chunk: 27.
Round 2 — look at 27.
- D: How many times does 4 go into 27? 4 × 6 = 24. 4 × 7 = 28 (too big). Answer: 6. Write 6 above the 7.
- M: 6 × 4 = 24.
- S: 27 − 24 = 3.
- B: Bring down the 2. New chunk: 32.
Round 3 — look at 32.
- D: How many times does 4 go into 32? Exactly 8 (4 × 8 = 32). Write 8.
- M: 8 × 4 = 32.
- S: 32 − 32 = 0.
- B: Nothing left to bring down. Done.
Answer: 672 ÷ 4 = 168 with no remainder.
Check: 168 × 4 = 672 ✓
4. Example 2 — 754 ÷ 6 (with a remainder)
Round 1 — 7 ÷ 6. 6 × 1 = 6. Write 1. 7 − 6 = 1. Bring down 5. New chunk: 15.
Round 2 — 15 ÷ 6. 6 × 2 = 12. Write 2. 15 − 12 = 3. Bring down 4. New chunk: 34.
Round 3 — 34 ÷ 6. 6 × 5 = 30. Write 5. 34 − 30 = 4. Nothing left to bring down.
Answer: 754 ÷ 6 = 125 R 4.
Check: 125 × 6 = 750, and 750 + 4 = 754 ✓
5. Example 3 — 305 ÷ 5 (zero in the middle of the quotient)
This example teaches an important habit: when the divisor doesn’t fit into the chunk, write a zero in the quotient and bring down the next digit. Don’t skip.
Round 1 — 3 ÷ 5. 5 does not fit into 3 (5 × 0 = 0). Write 0 above the 3. 3 − 0 = 3. Bring down 0. New chunk: 30.
Round 2 — 30 ÷ 5. 5 × 6 = 30. Write 6. 30 − 30 = 0. Bring down 5. New chunk: 5.
Round 3 — 5 ÷ 5. 5 × 1 = 5. Write 1. 5 − 5 = 0. Done.
Answer: 305 ÷ 5 = 61. (The leading 0 is silent when we write the final answer, but writing it during long division keeps the digits lined up.)
- Does the divisor fit into the first digit of the dividend? If not, group the first two digits together and start there.
- What multiplication fact is closest but not over? That gives you the next digit of the quotient.
- Is my subtraction result smaller than the divisor? If not, my quotient digit was too small — try one higher.
6. How to check every division answer
The division-check identity
dividend = divisor × quotient + remainder
This is just division re-expressed as multiplication and addition. It works for every long-division problem, whether or not there’s a remainder.
Example: 754 ÷ 6 = 125 R 4 ⇒ 6 × 125 + 4 = 750 + 4 = 754 ✓
Kid Einsteins students at SOMATH check every long-division answer using this identity. It catches almost every mistake.
7. Twenty-five practice questions — click to reveal each answer
All 25 problems are three-digit dividends divided by a one-digit divisor. Some divide evenly, some have remainders. Try them on paper first, then click Show answer to see the step-by-step solution and the check.
Q1
Divide: 248 ÷ 2
Show answer
Answer: 124
Round 1: 2 ÷ 2 = 1, remainder 0. Bring down 4.
Round 2: 4 ÷ 2 = 2, remainder 0. Bring down 8.
Round 3: 8 ÷ 2 = 4, remainder 0.
Check: 124 × 2 = 248 ✓
Q2
Divide: 369 ÷ 3
Show answer
Answer: 123
Each digit of 369 is divisible by 3 cleanly: 3÷3=1, 6÷3=2, 9÷3=3.
Check: 123 × 3 = 369 ✓
Q3
Divide: 672 ÷ 4
Show answer
Answer: 168
Same as Example 1 above. Round 1: 6÷4=1 r2. Round 2: 27÷4=6 r3. Round 3: 32÷4=8 r0.
Check: 168 × 4 = 672 ✓
Q4
Divide: 525 ÷ 5
Show answer
Answer: 105
Round 1: 5÷5=1. Round 2: 2÷5=0 (write 0, bring down 5). Round 3: 25÷5=5.
Check: 105 × 5 = 525 ✓ — note the zero in the middle.
Q5
Divide: 431 ÷ 3
Show answer
Answer: 143 R 2
Round 1: 4÷3=1 r1, bring down 3 → 13.
Round 2: 13÷3=4 r1, bring down 1 → 11.
Round 3: 11÷3=3 r2.
Check: 143 × 3 + 2 = 429 + 2 = 431 ✓
Q6
Divide: 754 ÷ 6
Show answer
Answer: 125 R 4
Same as Example 2 above.
Check: 125 × 6 + 4 = 750 + 4 = 754 ✓
Q7
Divide: 816 ÷ 8
Show answer
Answer: 102
Round 1: 8÷8=1. Round 2: 1÷8=0 (write 0, bring down 6). Round 3: 16÷8=2.
Check: 102 × 8 = 816 ✓ — zero in the tens place.
Q8
Divide: 589 ÷ 7
Show answer
Answer: 84 R 1
Round 1: 5÷7=0 — 7 doesn’t fit into 5. Group with the next digit → 58.
Round 2: 58÷7=8 r2 (7×8=56). Bring down 9 → 29.
Round 3: 29÷7=4 r1 (7×4=28).
Quotient is 84, remainder 1. (When the divisor doesn’t fit into the leading digit, the quotient has one fewer digit than the dividend.)
Check: 84 × 7 + 1 = 588 + 1 = 589 ✓
Q9
Divide: 936 ÷ 9
Show answer
Answer: 104
Round 1: 9÷9=1. Round 2: 3÷9=0 (write 0, bring down 6). Round 3: 36÷9=4.
Check: 104 × 9 = 936 ✓
Q10
Divide: 467 ÷ 5
Show answer
Answer: 93 R 2
Round 1: 5 doesn’t fit into 4 → group with 6 → 46.
Round 2: 46÷5=9 r1 (5×9=45). Bring down 7 → 17.
Round 3: 17÷5=3 r2 (5×3=15).
Check: 93 × 5 + 2 = 465 + 2 = 467 ✓
Q11
Divide: 378 ÷ 6
Show answer
Answer: 63
Round 1: 6 doesn’t fit into 3 → group with 7 → 37.
Round 2: 37÷6=6 r1 (6×6=36). Bring down 8 → 18.
Round 3: 18÷6=3 r0.
Check: 63 × 6 = 378 ✓
Q12
Divide: 823 ÷ 4
Show answer
Answer: 205 R 3
Round 1: 8÷4=2 r0. Bring down 2 → 2.
Round 2: 2÷4=0 (write 0, bring down 3) → 23.
Round 3: 23÷4=5 r3.
Check: 205 × 4 + 3 = 820 + 3 = 823 ✓ — zero in the middle of the quotient.
Q13
Divide: 648 ÷ 8
Show answer
Answer: 81
Round 1: 8 doesn’t fit into 6 → group with 4 → 64.
Round 2: 64÷8=8 r0. Bring down 8 → 8.
Round 3: 8÷8=1 r0.
Check: 81 × 8 = 648 ✓
Q14
Divide: 500 ÷ 7
Show answer
Answer: 71 R 3
Round 1: 7 doesn’t fit into 5 → group with 0 → 50.
Round 2: 50÷7=7 r1 (7×7=49). Bring down 0 → 10.
Round 3: 10÷7=1 r3.
Check: 71 × 7 + 3 = 497 + 3 = 500 ✓
Q15
Divide: 999 ÷ 4
Show answer
Answer: 249 R 3
Round 1: 9÷4=2 r1. Bring down 9 → 19.
Round 2: 19÷4=4 r3 (4×4=16). Bring down 9 → 39.
Round 3: 39÷4=9 r3 (4×9=36).
Check: 249 × 4 + 3 = 996 + 3 = 999 ✓
Q16
Divide: 720 ÷ 6
Show answer
Answer: 120
Round 1: 7÷6=1 r1. Bring down 2 → 12.
Round 2: 12÷6=2 r0. Bring down 0 → 0.
Round 3: 0÷6=0 r0.
Check: 120 × 6 = 720 ✓
Q17
Divide: 614 ÷ 9
Show answer
Answer: 68 R 2
Round 1: 9 doesn’t fit into 6 → group with 1 → 61.
Round 2: 61÷9=6 r7 (9×6=54). Bring down 4 → 74.
Round 3: 74÷9=8 r2 (9×8=72).
Check: 68 × 9 + 2 = 612 + 2 = 614 ✓
Q18
Divide: 896 ÷ 7
Show answer
Answer: 128
Round 1: 8÷7=1 r1. Bring down 9 → 19.
Round 2: 19÷7=2 r5 (7×2=14). Bring down 6 → 56.
Round 3: 56÷7=8 r0.
Check: 128 × 7 = 896 ✓
Q19
Divide: 305 ÷ 4
Show answer
Answer: 76 R 1
Round 1: 4 doesn’t fit into 3 → group with 0 → 30.
Round 2: 30÷4=7 r2 (4×7=28). Bring down 5 → 25.
Round 3: 25÷4=6 r1 (4×6=24).
Check: 76 × 4 + 1 = 304 + 1 = 305 ✓
Q20
Divide: 450 ÷ 5
Show answer
Answer: 90
Round 1: 5 doesn’t fit into 4 → group with 5 → 45.
Round 2: 45÷5=9 r0. Bring down 0.
Round 3: 0÷5=0 r0.
Check: 90 × 5 = 450 ✓
Q21
Divide: 777 ÷ 6
Show answer
Answer: 129 R 3
Round 1: 7÷6=1 r1. Bring down 7 → 17.
Round 2: 17÷6=2 r5 (6×2=12). Bring down 7 → 57.
Round 3: 57÷6=9 r3 (6×9=54).
Check: 129 × 6 + 3 = 774 + 3 = 777 ✓
Q22
Divide: 862 ÷ 3
Show answer
Answer: 287 R 1
Round 1: 8÷3=2 r2. Bring down 6 → 26.
Round 2: 26÷3=8 r2 (3×8=24). Bring down 2 → 22.
Round 3: 22÷3=7 r1 (3×7=21).
Check: 287 × 3 + 1 = 861 + 1 = 862 ✓
Q23
Divide: 504 ÷ 8
Show answer
Answer: 63
Round 1: 8 doesn’t fit into 5 → group with 0 → 50.
Round 2: 50÷8=6 r2 (8×6=48). Bring down 4 → 24.
Round 3: 24÷8=3 r0.
Check: 63 × 8 = 504 ✓
Q24
Divide: 201 ÷ 7
Show answer
Answer: 28 R 5
Round 1: 7 doesn’t fit into 2 → group with 0 → 20.
Round 2: 20÷7=2 r6 (7×2=14). Bring down 1 → 61.
Round 3: 61÷7=8 r5 (7×8=56).
Check: 28 × 7 + 5 = 196 + 5 = 201 ✓
Q25
Divide: 908 ÷ 9
Show answer
Answer: 100 R 8
Round 1: 9÷9=1 r0. Bring down 0 → 0.
Round 2: 0÷9=0 r0 (write 0). Bring down 8 → 8.
Round 3: 8÷9=0 r8 (9 doesn’t fit into 8, write 0).
Check: 100 × 9 + 8 = 900 + 8 = 908 ✓ — two zeros in the quotient.
8. Five challenge word problems
Real division problems from Kid Einsteins classes. Read carefully, decide what’s being asked, and try each on paper before revealing.
Q26 — Field trip buses
A school is taking 328 students on a field trip. Each bus can carry 6 students per row and has 8 rows. How many buses does the school need?
Show answer
Answer: 7 buses
Each bus holds 6 × 8 = 48 students.
Divide: 328 ÷ 48 — but we don’t know two-digit divisors yet. Instead: how many groups of 48 fit into 328? 48 × 6 = 288. 48 × 7 = 336 (too many). So 6 buses hold 288 students, leaving 328 − 288 = 40 students still standing at school. Those 40 students need one more bus, so the school needs 7 buses total.
Key idea: when a division problem asks “how many groups do you need?” and there’s a remainder, always round up. You can’t leave 40 students behind.
Q27 — Sharing candies
Ms. Chen has 435 candies to share equally among her 5 grandchildren. How many does each grandchild get, and how many candies are left over?
Show answer
Answer: 87 candies each, 0 left over
Divide 435 ÷ 5.
Round 1: 5 doesn’t fit into 4 → group with 3 → 43. 43÷5=8 r3. Bring down 5 → 35.
Round 2: 35÷5=7 r0.
Each grandchild gets 87 candies, and 0 are left over.
Check: 87 × 5 = 435 ✓
Q28 — Class supplies
A teacher has 250 pencils to put into boxes. Each box holds 8 pencils. How many full boxes can she fill, and how many pencils will be left over?
Show answer
Answer: 31 full boxes, 2 pencils left over
Divide 250 ÷ 8.
Round 1: 8 doesn’t fit into 2 → group with 5 → 25. 25÷8=3 r1 (8×3=24). Bring down 0 → 10.
Round 2: 10÷8=1 r2 (8×1=8).
Quotient 31 R 2 — so 31 full boxes and 2 pencils left over.
Check: 31 × 8 + 2 = 248 + 2 = 250 ✓
Q29 — Weekly savings
Sophia saved the same amount of money every week for 9 weeks and had $684 at the end. How much did she save each week?
Show answer
Answer: $76 per week
Divide 684 ÷ 9.
Round 1: 9 doesn’t fit into 6 → group with 8 → 68. 68÷9=7 r5 (9×7=63). Bring down 4 → 54.
Round 2: 54÷9=6 r0.
Sophia saved $76 each week.
Check: 76 × 9 = 684 ✓
Q30 — Bake sale trays
The PTA baked 815 cookies for a bake sale. They want to arrange them on trays with 7 cookies per tray. How many trays will be completely full, and how many extra cookies will be left over for the volunteers to eat?
Show answer
Answer: 116 full trays, 3 cookies for the volunteers
Divide 815 ÷ 7.
Round 1: 8÷7=1 r1. Bring down 1 → 11.
Round 2: 11÷7=1 r4. Bring down 5 → 45.
Round 3: 45÷7=6 r3 (7×6=42).
Quotient 116 R 3 — 116 full trays and 3 cookies left over.
Check: 116 × 7 + 3 = 812 + 3 = 815 ✓
9. Answer key
| # | Problem | Answer |
|---|---|---|
| Q1 | 248 ÷ 2 | 124 |
| Q2 | 369 ÷ 3 | 123 |
| Q3 | 672 ÷ 4 | 168 |
| Q4 | 525 ÷ 5 | 105 |
| Q5 | 431 ÷ 3 | 143 R 2 |
| Q6 | 754 ÷ 6 | 125 R 4 |
| Q7 | 816 ÷ 8 | 102 |
| Q8 | 589 ÷ 7 | 84 R 1 |
| Q9 | 936 ÷ 9 | 104 |
| Q10 | 467 ÷ 5 | 93 R 2 |
| Q11 | 378 ÷ 6 | 63 |
| Q12 | 823 ÷ 4 | 205 R 3 |
| Q13 | 648 ÷ 8 | 81 |
| Q14 | 500 ÷ 7 | 71 R 3 |
| Q15 | 999 ÷ 4 | 249 R 3 |
| Q16 | 720 ÷ 6 | 120 |
| Q17 | 614 ÷ 9 | 68 R 2 |
| Q18 | 896 ÷ 7 | 128 |
| Q19 | 305 ÷ 4 | 76 R 1 |
| Q20 | 450 ÷ 5 | 90 |
| Q21 | 777 ÷ 6 | 129 R 3 |
| Q22 | 862 ÷ 3 | 287 R 1 |
| Q23 | 504 ÷ 8 | 63 |
| Q24 | 201 ÷ 7 | 28 R 5 |
| Q25 | 908 ÷ 9 | 100 R 8 |
| Q26 | Field trip — 328 students, 48 per bus | 7 buses (round up) |
| Q27 | 435 candies ÷ 5 grandchildren | 87 each, 0 left |
| Q28 | 250 pencils ÷ 8 per box | 31 full boxes, 2 left |
| Q29 | $684 ÷ 9 weeks | $76 per week |
| Q30 | 815 cookies ÷ 7 per tray | 116 trays, 3 left |
10. FAQ
What if the divisor doesn’t fit into the first digit of the dividend?
Group the first two digits together and start there. For example, 378 ÷ 6 starts by asking “how many times does 6 fit into 37?” because 6 doesn’t fit into 3 alone. The quotient will have one fewer digit than the dividend.
What if the subtraction gives a number bigger than the divisor?
Your quotient digit was too small. Erase and try one higher. For example, if you’re dividing 27 by 4 and you write 5 as the quotient digit, 4 × 5 = 20 and 27 − 20 = 7 — but 7 is bigger than 4, so 4 fits again. The correct quotient digit is 6, not 5. The subtraction result must always be smaller than the divisor.
What does the remainder mean in a word problem?
It depends on the question. If you’re sharing candy and one candy is left over, you leave 1 as the remainder. If you’re asking “how many buses do we need?” and the remainder means students left standing, you must round up (rent one more bus). If you’re asking “how many full trays?” and the remainder is 3 cookies, those 3 don’t make a full tray — the answer is the quotient only. Always re-read the question after you get the numerical answer.
Do we ever divide by a two-digit divisor in Class 7?
Not yet. In Class 7 the divisor is always a single digit (2 through 9), and the dividend is up to three digits. Two-digit divisors come next year in the Young Fermats Pre-Algebra program (grades 5–6), where students meet larger multiplication estimates and long division with dividends up to five digits.
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