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Long Division: Divide-Multiply-Subtract-Bring Down

Long division breaks division into repeated steps: divide the working number by the divisor, multiply, subtract, bring down. The quotient is built digit by digit. Remainder is always less than the divisor. Verification: Qร—D+R=Dividend.

Concept Fundamentals
Number being divided
Dividend
Number dividing by
Divisor
Result
Quotient
Left over < divisor
Remainder

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Verification: Quotient ร— Divisor + Remainder = Dividend. The obelus รท was introduced by Johann Rahn in 1659. Decimal places extend the quotient for fractional results.

Key quantities
Number being divided
Dividend
Key relation
Number dividing by
Divisor
Key relation
Result
Quotient
Key relation
Left over < divisor
Remainder
Key relation

Ready to run the numbers?

Why: Long division handles large numbers that mental math cannot. Used in finance, measurement, sharing, and scaling. The algorithm is foundational for polynomial division.

How: Repeat: divide working number by divisor to get quotient digit; multiply that digit by divisor; subtract from working number; bring down next digit. Remainder is always less than divisor.

Verification: Quotient ร— Divisor + Remainder = Dividend.The obelus รท was introduced by Johann Rahn in 1659.
Sources:Khan AcademyMath is Fun

Run the calculator when you are ready.

Start Long DivisionEnter dividend and divisor

Enter Numbers

long_division.sh
CALCULATED
$ divide --dividend=100 --divisor=7
Quotient
14
Remainder
2
Decimal
14.28
Verification
Qร—D+R=โœ“
Long Division Calculator
100 รท 7 = 14 R 2
Decimal: 14.28
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Quotient vs Remainder

Quotient & Remainder Proportions

๐Ÿ“ Traditional Long Division Format

14
7) 100
โˆ’ 7
30
โˆ’ 28
2
Remainder: 2

๐Ÿ“‹ Step-by-Step (Divide-Multiply-Subtract-Bring Down)

Step 1
Bring down 1. 1 < 7, so we bring down the next digit.
Working: 1 โ†’ Quotient digit: 0 | Subtract: remainder 1 | Bring down: 0
Step 2
Divide: 7 goes into 10 exactly 1 time(s). Multiply: 7 ร— 1 = 7. Subtract: 10 โˆ’ 7 = 3. Bring down: 0.
Working: 10 โ†’ Quotient digit: 1 | Multiply: 7 ร— 1 = 7 | Subtract: remainder 3 | Bring down: 0
Step 3
Divide: 7 goes into 30 exactly 4 time(s). Multiply: 7 ร— 4 = 28. Subtract: 30 โˆ’ 28 = 2.
Working: 30 โ†’ Quotient digit: 4 | Multiply: 7 ร— 4 = 28 | Subtract: remainder 2
Verification:14 ร— 7 + 2 = 100 = 100 โœ“

๐Ÿ“ Step-by-Step Breakdown

INPUTS
Dividend
100
Divisor
7
RESULTS
Quotient
14
Remainder
2
100 mod 7
Decimal Result
14.28
to 2 decimal places
VERIFICATION
Verification
14 ร— 7 + 2 = 100 = 100 โœ“
Remainder as Fraction
2/7
2/7 simplified

For educational and informational purposes only. Verify with a qualified professional.

๐Ÿงฎ Fascinating Math Facts

รท

Dividend รท Divisor = Quotient R Remainder

โ€” Basic division

โœ“

Always verify: Qร—D+R=Dividend

โ€” Check your work

๐Ÿ“‹ Key Takeaways

  • โ€ข Long division breaks division into repeated divide, multiply, subtract, bring down steps
  • โ€ข The remainder is what's left when the divisor no longer fits โ€” always less than the divisor
  • โ€ข Verification: Quotient ร— Divisor + Remainder = Dividend
  • โ€ข Decimal places extend the quotient for fractional results (e.g., 100 รท 7 = 14.2857โ€ฆ)
  • โ€ข When the divisor doesn't fit, write 0 in the quotient and bring down the next digit

๐Ÿ’ก Did You Know?

๐Ÿ“Long division has been used since the 12th century. The modern algorithm was formalized in the 1600s.Source: Math History
รทThe division symbol รท is called an obelus. It was first used by Swiss mathematician Johann Rahn in 1659.Source: Etymology
โœ“Always verify: Quotient ร— Divisor + Remainder = Dividend. This catches calculation errors.Source: Best Practice
๐Ÿ“šLong division is the foundation for polynomial long division used in algebra and calculus.Source: Mathematics
โ†ปThe algorithm repeats: divide, multiply, subtract, bring down โ€” until all digits are processed.Source: Algorithm
RRemainder R is always less than the divisor. 100 รท 7 = 14 R 2, and 2 < 7.Source: Remainder Rule

๐Ÿ“– How Long Division Works

Long division is an algorithm that divides large numbers by repeatedly: (1) Divide the current working number by the divisor to get a quotient digit, (2) Multiply that digit by the divisor, (3) Subtract from the working number, (4) Bring down the next digit. Repeat until all digits are processed.

Verification

Quotient ร— Divisor + Remainder = Dividend. This confirms your answer is correct.

๐Ÿ“ Worked Example: 100 รท 7

Setup: Divide 100 by 7. Write 7 on the left, 100 under the bracket.

Step 1: 7 into 1? Zero. Bring down 0. Working: 10.

Step 2: 7 into 10? Once. Multiply: 7ร—1=7. Subtract: 10โˆ’7=3.

Step 3: Bring down 0. Working: 30.

Step 4: 7 into 30? Four times. Multiply: 7ร—4=28. Subtract: 30โˆ’28=2.

Result: Quotient = 14, Remainder = 2. So 100 รท 7 = 14 R 2, or 14.2857โ€ฆ as decimal.

Verification: 14 ร— 7 + 2 = 98 + 2 = 100 โœ“

๐Ÿš€ Real-World Applications

๐Ÿ’ฐ Finance & Splitting

Dividing bills, per-unit cost, profit per share, loan payments.

๐Ÿ“Š Data & Rates

Averages, rates per unit, percentages, scaling down.

๐Ÿ—๏ธ Construction

Tiles per row, materials per section, spacing calculations.

๐Ÿ›’ Retail

Price per unit, bulk discounts, inventory allocation.

๐Ÿ”ฌ Science

Concentrations, rates, unit conversions, ratios.

โฑ๏ธ Time & Speed

Distance รท time = speed, work รท rate = time.

โš ๏ธ Common Mistakes to Avoid

  • Forgetting the remainder: Always check if there is a remainder. 100 รท 7 = 14 R 2, not just 14.
  • Wrong quotient digit: Use the largest multiple of the divisor that fits. For 30 รท 7, use 4 (7ร—4=28), not 3 or 5.
  • Not verifying: Always verify: Quotient ร— Divisor + Remainder = Dividend.
  • Division by zero: Never divide by 0. It is undefined.
  • Misaligning digits: Keep the quotient digits aligned above the correct dividend digits.

๐ŸŽฏ Expert Tips

๐Ÿ’ก Estimate First

Before dividing, estimate. For 100 รท 7, 7ร—14=98, so quotient โ‰ˆ 14. Helps catch errors.

๐Ÿ’ก Remainder as Fraction

Enable "Show remainder as fraction" to see remainder in lowest terms. E.g., 2/7 for 100รท7.

๐Ÿ’ก Decimal Places

For repeating decimals, increase decimal places to see the pattern. 1รท3 = 0.333โ€ฆ

๐Ÿ’ก Zero in Quotient

When the divisor doesn't fit, write 0 and bring down the next digit. E.g., 56 doesn't fit into 12.

๐Ÿ“Š Reference Table

ExampleQuotientRemainder
100 รท 7142
1234 รท 56222
999 รท 33330
50000 รท 12340662
7 รท 321
144 รท 12120

๐Ÿ“ Quick Reference

รท
Obelus symbol
R
Remainder notation
0-10
Decimal places
โœ“
Qร—D+R=Dividend

๐ŸŽ“ Practice Problems

156 รท 12 โ†’ Answer: 13 R 0
89 รท 6 โ†’ Answer: 14 R 5
1000 รท 8 โ†’ Answer: 125 R 0
50 รท 7 โ†’ Answer: 7 R 1

โ“ FAQ

What is the remainder in long division?

The remainder is the amount left over after the divisor has been subtracted as many times as possible from the dividend. It is always less than the divisor.

How do I get a decimal result?

Use Advanced mode and increase "Decimal places". The calculator continues division by appending zeros to the remainder and computing more digits.

Why does verification matter?

Verification (Quotient ร— Divisor + Remainder = Dividend) proves your division was performed correctly. If it doesn't check out, there was an error.

What is the difference between quotient and remainder?

The quotient is how many times the divisor fits. The remainder is what is left. For 100รท7, quotient=14, remainder=2 โ€” 7 fits 14 times with 2 left.

When should I use remainder as fraction?

Enable "Show remainder as fraction" in Advanced mode for fractional form. E.g., 100รท7 gives 2/7, so exact result is 14 2/7.

Can I divide by decimals?

This calculator uses integers only. For decimal division, multiply both by a power of 10 to make them integers, then divide and adjust.

What is the divide-multiply-subtract-bring down cycle?

The core long division loop: (1) Divide working number by divisor, (2) Multiply quotient digit by divisor, (3) Subtract from working number, (4) Bring down next digit. Repeat.

๐Ÿ“Œ Summary

Long division divides large numbers using the repeated cycle: divide, multiply, subtract, bring down. The quotient is built digit by digit. The remainder is always less than the divisor. Verification (Qร—D+R=Dividend) confirms correctness. Decimal places extend the result for fractional answers. Master this algorithm for arithmetic fluency and as a foundation for polynomial division.

โœ… Verification Tip

Always verify: Quotient ร— Divisor + Remainder = Dividend. Estimate first โ€” e.g., 100รท7 โ‰ˆ 14 โ€” to catch major errors. For exact division (remainder 0), multiply quotient by divisor to confirm.

๐Ÿ”— Next Steps

After mastering long division, try the Long Multiplication Calculator for the inverse operation, or the Remainder Calculator for modulo. The Long Addition Calculator helps with the subtraction step.

โš ๏ธ Disclaimer: This calculator performs integer division. For very large numbers, JavaScript number precision limits may apply. Results are for educational purposes. Always verify critical calculations.

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