Introduction to Long Division

Introduction to Long Division

• Long division is a method for dividing large numbers accurately.
• It's used when the divisor isn't a simple one-digit number or a multiple of ten.
• The process breaks down the division into manageable steps.
• The method mirrors repeated subtraction in division.

Setting up a Long Division Problem

• Place the dividend inside the division symbol.
• Write the divisor outside the division symbol.

Steps in Long Division

• Divide: Determine the divisor's count in the dividend's initial digits. Write the result above the dividend.
• Multiply: Multiply the divisor by the quotient digit. Write the result below the relevant portion of the dividend.
• Subtract: Subtract the product from the corresponding portion of the dividend.
• Bring Down: Bring down the next digit of the dividend to the right of the remainder.
• Repeat: Repeat steps 1-4 until all dividend digits are processed.

Remainders and Decimals

• If a remainder appears, express it as a fraction, decimal, or simply state the remainder.
• To express a remainder as a decimal, append zeroes to the dividend for further decimal places until there's no remainder.
• Use appropriate notation for repeating decimals.

Example

• Dividing 5,248 by 12:

  • Setup: 12 | 5,248

  • Divide 12 into 52 (first two digits): 12 goes into 52 four times (4 x 12 = 48).

  • Write 4 above the 2 in the dividend.

  • Subtract: 52 - 48 = 4.

  • Bring down 4: 44.

  • Divide 12 into 44: 12 goes into 44 three times (3 x 12 = 36).

  • Write 3 above the 4 in the dividend.

  • Subtract: 44 - 36 = 8.

  • Bring down 8: 88.

  • Divide 12 into 88: 12 goes into 88 seven times (7 x 12 = 84).

  • Write 7 above the 8 in the dividend.

  • Subtract: 88 - 84 = 4.

  • The result is 437 with a remainder of 4. (437 4/12, which simplifies to 437 1/3, or 437.333...)

Strategies for Long Division Simplification

• Estimating: Round numbers to estimate the initial quotient, ensuring accuracy.
• Chunking/Breaking Numbers: Break down the dividend into parts using numbers easier to compute.

Long Division Use Cases

• Long division is essential for various applications including:
• Basic arithmetic calculations.
• Everyday activities like budgeting, shopping, or planning.
• More advanced fields such as statistics, algebra, geometry, and technical areas.