A Step-by-Step Guide to Long Division

Long division is a standard algorithm used for dividing multi-digit numbers. It breaks down a complex division problem into a series of smaller, more manageable steps. While it may seem daunting at first, it is a systematic and reliable method for finding a quotient and a remainder. This calculator not only provides the final answer but also visualizes each step of the process, making it an excellent learning tool for students and a quick verification tool for anyone who needs it.

The Vocabulary of Division

To understand the process, let's first define the terms:

• Dividend: The number that is being divided (the number inside the division bracket).
• Divisor: The number that you are dividing by (the number outside the bracket).
• Quotient: The result of the division, or how many times the divisor goes into the dividend (the number written on top).
• Remainder: The amount 'left over' after the division is complete.

The Long Division Algorithm: Divide, Multiply, Subtract, Bring Down

The process of long division can be remembered with the simple mnemonic: **D**ivide, **M**ultiply, **S**ubtract, **B**ring down. You repeat these four steps until the problem is complete.

1. Divide: Look at the first digit (or first few digits) of the dividend and determine how many times the divisor can go into it without exceeding it. Write this number (the first digit of the quotient) on top of the division bracket.
2. Multiply: Multiply the quotient digit you just found by the divisor. Write this product directly underneath the part of the dividend you were just working with.
3. Subtract: Subtract the product you just calculated from the dividend part above it. Write the result of the subtraction directly below.
4. Bring Down: Bring down the next digit from the dividend and write it next to the result of your subtraction. This forms the new number you will work with.

You repeat this four-step cycle until there are no more digits to bring down from the dividend. The final number left after the last subtraction is your remainder.

Example: 1234 ÷ 5

• Step 1: Look at 12. 5 goes into 12 two times. Write '2' as the first digit of the quotient.
• Step 2: Multiply 2 × 5 = 10. Write 10 under the 12.
• Step 3: Subtract 12 - 10 = 2.
• Step 4: Bring down the next digit, '3', to make the new number 23.
• Repeat Cycle: How many times does 5 go into 23? Four times. Write '4' as the next quotient digit. Multiply 4 × 5 = 20. Subtract 23 - 20 = 3. Bring down the next digit, '4', to make 34.
• Repeat Cycle: How many times does 5 go into 34? Six times. Write '6' as the next quotient digit. Multiply 6 × 5 = 30. Subtract 34 - 30 = 4.
• Finish: There are no more digits to bring down. The final quotient is 246, and the remainder is 4.