How to Do Long Division with Stepwise Method and Solved Examples
Long division in arithmetic is a common division algorithm suitable for multi-digit number splitting that is easy enough to do by hand. It breaks down a problem with a division into a set of easier measures.
One number, called the dividend, is split by another, called the divisor, producing a result called the quotient, as in all division issues. It makes it possible to perform computations involving arbitrarily large numbers by following a series of simple steps. Chunking (also referred to as the method of partial quotients or the hangman method) is a less mechanical type of long division prominent in the United Kingdom that leads to a more holistic understanding of the process of division.
(Image will be uploaded soon)
Define Long Division
When you divide a large number (typically three-digits or more) by a two-digit (or more) number, the long division method is used. Similar to short division (the 'bus stop' technique), it is set out. Long division does not use the division slash or division sign symbols in English-speaking countries but instead constructs a tableau. The divisor is separated by a right parenthesis from the dividend (or vertical bar); the dividend is separated by a vinculum from the quotient (i.e., an overbar). Long division is a mathematical operation which allows you to use a pencil and paper to perform complex division problems. The more complicated problem is broken down into simpler measures. With the advancements in computers and calculators, the need to know long division has faded. It is a valuable ability to have, however, and an outstanding way to exercise the brain.
Long Division Steps
In solving a long division problem, there are four main steps:
Division.
Multiplying.
Minus.
Drop the last digit.
Long division is a method where the aim of each step is to simplify the next step, with each step we acquire one digit of the quotient and by the end of the process, we get the quotient.
Step 1: Divide the dividend of ten columns by the divisor.
Step 2: In the ten position column, multiply the divider by the quotient.
Step 3: Subtract the divider from the element.
Step 4: In the column, put the dividend down and repeat.
Step 5: To keep it simple, start with one-digit dividers and two-digit dividends.
(Image will be uploaded soon)
Division Types
Chunking: In primary school mathematics education, chunking (sometimes also referred to as the form of partial quotients) is an elementary approach to solving basic division issues by repeated subtraction. With the addition of a line separating the divisor, dividend, and partial quotients, it is also known as the hangman form. It also has a counterpart for multiplication in the grid method.
Formal Long Division: Long division helps to split the problem of division into a series of simpler steps. A large number, which is the dividend, is divided by another number, which is called the divisor, just like all division problems, to give a result called the quotient and sometimes a remainder.
(Image will be uploaded soon)
Long Division Examples
1. Using Long division, solve the following :
(Image will be uploaded soon)
Answer:
(Image will be uploaded soon)
(Image will be uploaded soon)
Answer :
(Image will be uploaded soon)
(Image will be uploaded soon)
Answer:
(Image will be uploaded soon)
FAQs on Long Division Method Explained Step by Step
1. What is long division in maths?
Long division is a method of dividing large numbers by breaking the division process into a series of easier steps. It is used when dividing numbers with two or more digits.
- It separates the division into manageable parts.
- It follows the sequence: Divide → Multiply → Subtract → Bring down.
- It can give a quotient with or without a remainder.
2. How do you do long division step by step?
Long division is done using the steps Divide, Multiply, Subtract, and Bring Down. Follow these steps:
- Divide the first digit(s) of the dividend by the divisor.
- Multiply the divisor by the result.
- Subtract to find the remainder.
- Bring down the next digit and repeat.
- 8 ÷ 4 = 2
- 2 × 4 = 8
- 8 − 8 = 0
- Bring down 4 → 4 ÷ 4 = 1
3. What is the long division formula?
The key formula for long division is Dividend = Divisor × Quotient + Remainder. This formula checks whether your division is correct.
- Dividend = number being divided
- Divisor = number you divide by
- Quotient = result
- Remainder = leftover value
4. How do you do long division with remainders?
Long division with remainders means the final subtraction leaves a number smaller than the divisor. The remainder is what is left after the last step.
- Divide as usual.
- Stop when no digits remain to bring down.
- If the leftover number is smaller than the divisor, it is the remainder.
- 3 goes into 17 five times (3 × 5 = 15)
- 17 − 15 = 2
5. How do you do long division with decimals?
Long division with decimals is done by placing the decimal point directly above in the quotient and dividing as usual. Follow these steps:
- If the divisor is a decimal, multiply both numbers to make it a whole number.
- Place the decimal point in the quotient above the dividend’s decimal.
- Continue dividing normally.
6. How do you do long division with a two-digit divisor?
Long division with a two-digit divisor follows the same steps but may require estimation. You divide, multiply, subtract, and bring down carefully.
- Estimate how many times the divisor fits into the first part of the dividend.
- Multiply and subtract.
- Bring down the next digit and repeat.
- 12 goes into 96 exactly 8 times
7. What is the difference between long division and short division?
The main difference is that long division shows all steps, while short division uses a compact method for easier calculations.
- Long division: best for larger numbers and multi-digit divisors.
- Short division: quicker method, often used for single-digit divisors.
8. Can you give an example of a long division problem with solution?
Yes, here is a solved long division example: 125 ÷ 5 = 25.
- 5 goes into 12 two times (2 × 5 = 10)
- 12 − 10 = 2
- Bring down 5 → 25
- 5 goes into 25 five times (5 × 5 = 25)
- 25 − 25 = 0
9. Why is long division important in maths?
Long division is important because it helps students divide large and complex numbers accurately. It builds understanding of place value and division concepts.
- Develops strong arithmetic skills.
- Prepares learners for fractions, decimals, and algebra.
- Used in real-life calculations like money and measurements.
10. What are common mistakes in long division?
Common mistakes in long division include incorrect subtraction, wrong placement of digits, and forgetting to bring down numbers. Avoid these errors:
- Not estimating correctly before dividing.
- Forgetting to write the remainder.
- Misplacing the decimal point in decimal division.
- Skipping steps in the divide–multiply–subtract process.
