Introduction to Long Division

Introduction to Long Division

• Long division is a method for dividing large numbers step-by-step to find the quotient and remainder.
• It's crucial for dividing multi-digit numbers efficiently.

Setting Up the Problem

• Arrange the dividend (the number being divided) inside the division symbol.
• Place the divisor (the number dividing) outside the symbol.
• Example: To divide 723 by 3, the setup is: 3 | 723

Dividing the First Digit(s)

• Begin by dividing the divisor into the initial digit(s) of the dividend.
• Estimate the quotient for the first division.
• Place the quotient above the corresponding digit(s) in the dividend.
• Multiply the divisor by the estimated quotient.
• Write the result below the corresponding part of the dividend.
• Subtract this result from the part of the dividend being used.

Bringing Down the Next Digit

• Bring down the next digit from the dividend to the right of the result of the subtraction.
• This combined value forms the new number for the next step of division.

Repeating the Process

• Repeat steps 2-4 until all digits of the dividend have been processed.
• Continue dividing the divisor into the new number from step 3.
• Record all quotients above the dividend to track the steps.

Finding the Remainder

• Check for a remainder after all the digits have been processed.
• If the result from the subtraction is 0 or less than the divisor, this value is the remainder.
• If the result of the subtraction is greater than the divisor, return to step 2 with the new number.

Example

• Dividing 128 by 4:
• Setup: 4 | 128
• Divide 4 into 12 (the first part of the dividend): 12 / 4 = 3 Place 3 above the 2.
• Multiply 4 by 3: 4 * 3 = 12. Place 12 under the 12.
• Subtract 12 from 12: 12 - 12 = 0. Place 0. Bring down the 8.
• Divide 4 into 8 (the new number): 8 / 4 = 2. Place 2 above the 8.
• Multiply 4 by 2: 4 * 2 = 8. Place 8 under the 8.
• Subtract 8 from 8: 8 - 8 = 0.
• No remainder; the answer is 32.

Understanding Quotient and Remainder

• The quotient is the result of the division.
• The remainder is the remaining value if the division does not result in an exact whole number.
• Example: 135 / 4 = 33 with a remainder of 3. This can be expressed as 135 = (4 * 33) + 3.