Long Division Step-by-Step (with Remainders & 2-Digit)
Divisor 6 โ 738 Dividend ย โย Remainder R 0
โข ๐ฉ Mom (Multiply): Quotient digit ร Divisor
โข ๐ง Sister (Subtract): Find leftover difference
โข ๐ฆ Brother (Bring down): Drop next single digit
โข ๐ถ Rover (Repeat/Remainder): Loop until done!
| Problem Type | Step-by-Step Long Division Stack | Answer & Proof Check |
|---|---|---|
| 1. Clean Division 738 รท 6 | 7รท6=1 โ 1ร6=6 โ 7-6=1 โ Drop 3 โ 13 13รท6=2 โ 2ร6=12 โ 13-12=1 โ Drop 8 โ 18 18รท6=3 โ 3ร6=18 โ 18-18=0 (Done!) | = 123 Check: 123 ร 6 = 738 โ |
| 2. With Remainder 845 รท 4 | 8รท4=2 โ 2ร4=8 โ 8-8=0 โ Drop 4 โ 4 4รท4=1 โ 1ร4=4 โ 4-4=0 โ Drop 5 โ 5 5รท4=1 โ 1ร4=4 โ 5-4=1 (Remainder R1) | = 211 R 1 211 ร 4 + 1 = 845 โ |
| 3. Zero in Middle 612 รท 3 | 6รท3=2 โ 2ร3=6 โ 6-6=0 โ Drop 1 โ 1 1รท3=0 (WRITE 0 ON TOP!) โ Drop 2 โ 12 12รท3=4 โ 4ร3=12 โ 12-12=0 | = 204 204 ร 3 = 612 โ |
(211 ร 4) + 1 = 844 + 1 = 845. If the result equals your original number, you are 100% correct!Long Division Step-by-Step: The DMSB Family Method & Visual Scaffold
Why We Divide Left-to-Right (The Fair Sharing Principle)
Unlike addition and multiplication (which start on the right with the smallest ones digit), division always starts on the LEFT with the biggest bills (Hundreds / Thousands).
If you have $738 to share among 6 people: You first give each person one $100 bill (6 ร 1 = $600 shared, with $100 left over). You change that leftover $100 into tens to make $130, share the tens, and finally share the ones!
The 4 Steps Every Child Learns: Dad, Mom, Sister, Brother
Memorize this family to solve any long division problem step-by-step:
Interactive Step-by-Step Long Division Stack
3-Digit by 1-DigitHow many times does 6 fit into 7? Exactly 1 time. Write 1 on top. Multiply 1 ร 6 = 6. Subtract 7 - 6 = 1. Bring down the 3 to make 13.
The 3 Mistakes That Cost Students Marks in Long Division
When you bring down a digit and the divisor fits 0 times, you MUST write 0 in the quotient! E.g., 612 รท 3 = 204. Forgetting this zero gives the wrong answer 24.
If your subtraction leftover is equal to or larger than your divisor, you underestimated your quotient digit. Increase it by 1!
Never bring down two digits in a single step without placing a 0 in the quotient first.
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3 Step-by-Step Worked Examples
Master the exact derivation across 1-digit divisors, remainders, and 2-digit divisors:
๐ฏ Active Recall Quiz (Test Your Long Division Mastery)
Test your long division skills with 3 quick questions. Instant feedback provided:
Frequently Asked Questions
DMSB is the famous family memory aid for the 4 core steps of long division: Dad = Divide, Mom = Multiply, Sister = Subtract, Brother = Bring down, and Rover (the dog) = Repeat or Remainder.
When you bring down a digit and the divisor cannot fit into it (0 times), you MUST place a 0 in the quotient directly above that digit before bringing down the next digit. Forgetting this 0 is the #1 most common student error (e.g. 612 รท 3 = 204, NOT 24).
Use the universal checking formula: (Quotient ร Divisor) + Remainder = Dividend. If this calculation equals your original starting number, your answer is 100% correct.
No! If your remainder after subtracting is equal to or larger than your divisor, you underestimated your quotient digit. Increase the quotient digit by 1 and subtract again.
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