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Last updated on August 26, 2025
Long division is a method of dividing large numbers by breaking them down into a series of easier steps. It involves division, multiplication, and subtraction, following a specific sequence to obtain the quotient and remainder. In this topic, we will learn the formula for long division.
Long division breaks down a division problem into a series of easier steps.
Let’s learn the systematic approach to perform long division.
Long division involves a sequence of steps: divide, multiply, subtract, bring down, and repeat until completion. The process is as follows:
1. Divide: Determine how many times the divisor fits into the current dividend portion.
2. Multiply: Multiply the divisor by the quotient found in the divide step.
3. Subtract: Subtract the result of the multiplication from the current dividend portion.
4. Bring down: Bring down the next digit of the dividend.
5. Repeat: Repeat the process until all digits have been used.
In long division, the dividend is the number being divided, the divisor is the number you are dividing by, the quotient is the result of the division, and the remainder is what is left over.
The formula for completing a division problem is: Dividend = (Divisor × Quotient) + Remainder
Long division is crucial in mathematics as it simplifies the division of large numbers:
- It provides a systematic method to obtain accurate results.
- It is foundational for understanding polynomial division and other advanced mathematical concepts.
- It aids in developing problem-solving skills and logical thinking.
Students often find long division challenging, but with practice and some tricks, it can become easier:
- Break down the problem into smaller parts and focus on one step at a time.
- Practice using different numbers to become familiar with the process.
- Use estimation to quickly determine the quotient in each step.
- Double-check each subtraction step to ensure accuracy.
Long division is used in various real-life scenarios to solve problems:
- Splitting a bill among friends to determine how much each person should pay.
- Dividing a quantity of items equally among groups.
- Calculating the average or finding proportions in recipes or construction projects.
Students make errors when performing long division. Here are some mistakes and the ways to avoid them to master long division.
Divide 125 by 5 using long division.
The quotient is 25
1. Divide: 5 goes into 12 twice (2), since 5 x 2 = 10
2. Subtract: 12 - 10 = 2
3. Bring down the next digit: 5, making it 25
4. Divide: 5 goes into 25 five times (5), since 5 x 5 = 25
5. Subtract: 25 - 25 = 0 Therefore, 125 ÷ 5 = 25.
Divide 364 by 4 using long division.
The quotient is 91
1. Divide: 4 goes into 36 nine times (9), since 4 x 9 = 36
2. Subtract: 36 - 36 = 0
3. Bring down the next digit: 4
4. Divide: 4 goes into 4 once (1), since 4 x 1 = 4
5. Subtract: 4 - 4 = 0
Therefore, 364 ÷ 4 = 91.
Divide 729 by 3 using long division.
The quotient is 243
1. Divide: 3 goes into 7 twice (2), since 3 x 2 = 6
2. Subtract: 7 - 6 = 1
3. Bring down the next digit: 2, making it 12
4. Divide: 3 goes into 12 four times (4), since 3 x 4 = 12
5. Subtract: 12 - 12 = 0
6. Bring down the next digit: 9
7. Divide: 3 goes into 9 three times (3), since 3 x 3 = 9
8. Subtract: 9 - 9 = 0
Therefore, 729 ÷ 3 = 243.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.