By Sandy Fleming – Updated August 30, 2022
Long division can seem daunting at first glance, but it is simply a systematic method for solving large division problems. Mastery of basic multiplication and division facts, as well as subtraction and regrouping, is essential for smooth execution. By following each step carefully and aligning numbers precisely, students can achieve reliable results.
1. Draw the long‑division symbol (a right‑facing parenthesis with a horizontal line).
2. Write the dividend (the number to be divided) inside the symbol. For example, in “558 ÷ 9,” the 558 is placed below the line.
3. Place the divisor (the number that divides) to the left of the symbol. In the example, 9 sits to the left of the parenthesis.
1. Begin with the leftmost digit of the dividend. If the divisor is larger, combine the next digit to form a two‑digit number. Repeat until the selected number exceeds the divisor. For 558 ÷ 9, 5 is smaller, so we use 55.
2. Divide the selected number by the divisor and write the quotient above the last digit considered. In the example, 55 ÷ 9 = 6, so 6 is placed above the second 5.
3. Multiply the divisor by the quotient digit and write the product beneath the selected digits. 9 × 6 = 54, written under 55.
4. Subtract the product from the selected number. 55 – 54 = 1. Bring down the next digit of the dividend. The new number to consider is 18.
5. Repeat steps 2‑4 until all digits of the dividend have been processed. The final quotient is the number written above the division symbol.
• Uneven division: When a remainder exists, write the remainder after the final subtraction and attach “R.” Convert the remainder to a fraction (remainder ÷ divisor) or extend the result to a decimal by appending zeros and continuing the division process.
• Large divisors: Use rounding or estimation. For example, 6 482 ÷ 31 can be approximated by rounding to 30 and 6 500, giving an initial guess of 2. Refine by continuing the long‑division steps.
• Decimal divisors: Shift the decimal point in both divisor and dividend to convert the divisor to a whole number. Then proceed with standard long division and adjust the decimal point in the final quotient accordingly.
• Write the problem on graph paper to keep columns perfectly aligned.
• Double‑check each subtraction to ensure no arithmetic errors creep in.
• Practice with a variety of examples, including those with remainders, fractions, decimals, and large numbers.
