Long division

Long division is a method of dividing two numbers, usually one larger number (the dividend) by another smaller number (the divisor), to find the quotient and remainder. This method breaks down the division process into smaller, more manageable steps. I will show here long division the way I was thought and this method makes more sense to me then the ones I saw teach in schools on the West. It is faster and more logical, and intuitive.

Here’s a step-by-step explanation of how long division works:

Example: 642 divided by 3.

Step 1: Divide

• Write the dividend (642) on the left side of the long division symbol (|). We use to use normal division symbol in this process but for sake of the clarity and differentiation from regular division I will use this symbol (|).
• Write the divisor (3) on the right side the symbol.
• All of that is on the left side of the equal sign.

642 | 3 =

Step 2: Estimate

• Estimate how many times the divisor (3) goes into the leftmost digit of the dividend (6). The estimate is 2 (2 × 3 = 6).
• Write this estimate after the equality sign. There are no reminders so don’t right anything under the 6, unless for practise. In that case right 0 under the 6 (first digit of the dividend).

642 | 3 = 2
0

Step 3: Bring down next dividend digit and repeat

• Bring down next dividend digit (4).
• Estimate how many times the divisor (3) goes into the new digit (4). It goes once (1).
• Write down 1 on the right side equal sign after digit 2.
• Write the reminder (1) under the the number 4 in the new, third row. Zero is not necessary but for the sake of the clarity I am keeping it in this example.

642 | 3 = 21
04
01

Step 4: Bring down next dividend digit and repeat

• Bring down next dividend digit (2).
• Estimate how many times the divisor (3) goes into the new digit (12). It goes four times (4).
• Write down 4 on the right side of the equal sign after digit 1.
• There are no more reminders so final result is 214.

642 | 3 = 214
04
012
000

NOTE: This process is repeated until there are no more reminders left. In the case of non-terming decimals (decimal number that continues endlessly) this never happens.