Division using long method

Introduction

Division is the mathematical process of sharing or grouping a number into equal parts. When we deal with large numbers that are difficult to divide mentally, we use the Long Division method. This method breaks the division process into smaller, organized steps to find how many times one number fits into another.

Key Points

1. Important Terms in Division

To master long division, you must know these four terms:

• Dividend: The large number you want to divide (placed inside the bracket).
• Divisor: The number you are dividing by (placed outside the bracket).
• Quotient: The answer you get after dividing.
• Remainder: The amount left over that cannot be divided further.

2. Steps for Long Division (DMSB)

We follow a repetitive cycle to solve long division problems:

1. D - Divide: See how many times the divisor goes into the first digit(s).
2. M - Multiply: Multiply the divisor by the number you just wrote in the quotient.
3. S - Subtract: Subtract that result from the dividend part.
4. B - Bring Down: Bring down the next digit of the dividend and repeat.

3. Worked Example

Question: Divide 432 by 3 ($432 \div 3$)

• Step 1 (Divide): How many 3s are in 4? 1. Write 1 on top.
• Step 2 (Multiply): $3 \times 1 = 3$. Write 3 under the 4.
• Step 3 (Subtract): $4 - 3 = 1$.
• Step 4 (Bring Down): Bring down the 3 to make 13.
• Repeat:
  • How many 3s in 13? 4. ($3 \times 4 = 12$).
  • Subtract: $13 - 12 = 1$.
  • Bring down the 2 to make 12.
  • How many 3s in 12? 4. ($3 \times 4 = 12$).
  • Subtract: $12 - 12 = 0$.

Final Answer (Quotient): 144

Brief Summary

Long division is a step-by-step technique used to divide large numbers by following the sequence: Divide, Multiply, Subtract, and Bring down. By repeating these steps until all digits of the dividend are used, we find our final answer (the quotient) and any remaining value (the remainder).