Division (longer)

Long division is a more detailed method of division that helps you divide larger numbers step by step. It’s used when the numbers are bigger or more complex than what short division can handle.

Steps for Long Division:

1. Write the Dividend and Divisor: Write the dividend (the number you want to divide) inside the long division symbol, and the divisor (the number you're dividing by) outside.
2. Divide the First Digit: Start by dividing the first digit (or the first few digits) of the dividend by the divisor. If the divisor doesn’t go into the first digit, you take the next digit as well.
3. Multiply: After dividing, multiply the divisor by the number you just found.
4. Subtract: Subtract the result of that multiplication from the portion of the dividend you divided.
5. Bring Down the Next Digit: Bring down the next digit of the dividend and repeat the process until all digits have been used.
6. Repeat: Continue the process until you’ve divided through all digits.
7. Write the Quotient: The numbers you wrote above the division symbol form the quotient (the result of the division). If there is any remainder, it will be written at the end.

Example: 145 ÷ 5

1. Divide the first digit (1):
   • 5 doesn’t go into 1, so we move to the next two digits (14).
   • 5 goes into 14 2 times (2 x 5 = 10).
   • Write 2 above the 4.
   • 14 - 10 = 4. Write 4 below the 14.
2. Bring down the next digit (5):
   • Now, you have 45.
   • 5 goes into 45 9 times (9 x 5 = 45).
   • Write 9 above the 5.
   • 45 - 45 = 0. No remainder left.

Subtract 45 from 45:

5 | 145
  2  9
------
  0

Divide 45 by 5:

5 | 145
  2  9

Subtract 10 from 14:

5 | 145
  2
----
  4

Divide 14 by 5:

5 | 145
  2

Set up the division:

5 | 145

Final Answer: 145 ÷ 5 = 29.

Key Things to Remember in Long Division:

• Multiplication: You multiply the divisor by the number you got from dividing, and subtract that from the dividend.
• Remainder: If you can't divide evenly, the leftover part is the remainder.
• Bring down: Always bring down the next digit when dividing step by step.

With practice, long division becomes much quicker!