How to Do Long Division: Step-by-Step Guide & Examples [With Worksheets]

Ever wondered how to tackle those dauntingly large math problems? How to navigate through numbers that seem like a maze? Fear not! Today, we’re diving into the realm of long division. From understanding its core principles to mastering the step-by-step process, we’ll equip you with the skills needed to conquer any numerical challenge. Whether you’re a student grappling with homework or an adult needing to crunch numbers, learning how to do long division is an invaluable skill.

So, are you ready to unravel the mysteries of long division and emerge victorious? Let’s embark on this mathematical journey together.

Here are some worksheets to help you practice long division. You can download them if you need them. Such as “Math Worksheets PDF: 30Math Olympiad Exercise for Grade 2-4″, and “Financial Literacy Books for Kids“, “40 Primary School Maths Problems Workbsheets PDF With Answers“, etc.

Understanding Long Division

Long division is a fundamental arithmetic operation that divides large numbers into smaller, more manageable parts. It is a methodical approach that efficiently divides numbers with multiple digits. At its core, long division involves several key components and concepts:

Definition: 

Long division is a mathematical process used to divide a dividend (the number being divided) by a divisor (the number doing the dividing) to obtain a quotient (the result) and, optionally, a remainder.

Objective: 

The primary objective of long division is to systematically break down a complex division problem into simpler steps, allowing for more straightforward computation.

Components of Long Division

Long division involves several essential components/parts that play distinct roles in the division process:

1. Dividend: This represents the number being divided. It is the larger number in the division problem and is divided by the divisor.
2. Divisor: The divisor is the number by which the dividend is divided. It is the smaller number in the division problem and is the divisor.
3. Quotient: The quotient is the result of dividing the dividend by the divisor. It represents how many times the divisor can be subtracted from the dividend.
4. Remainder: In cases where the dividend is not evenly divisible by the divisor, there may be a remainder left over after performing the division. The remainder represents the amount left over that cannot be evenly divided by the divisor.

Process Overview: 

The long division typically involves steps, including division, multiplication, subtraction, and bringing down digits. These steps are repeated until the entire dividend is divided or the desired precision level is achieved.

Importance: 

Long division is a fundamental skill in mathematics, laying the groundwork for more advanced mathematical concepts. It is commonly used in various real-world scenarios, such as budgeting, calculating proportions, and solving mathematical problems in fields like science, engineering, and finance.

Mastering Long Division: A Step-by-Step Guide

Long division may appear daunting at first, but breaking it down into manageable steps can make the process much more approachable. Let’s walk through each stage of long division, accompanied by clear examples:

Step 1: Divide

Begin by setting up the long division problem, with the dividend inside the division symbol and the divisor outside.

Start dividing from the leftmost digit of the dividend.

Example: Divide 735 by 5.

Step 2: Multiply

Multiply the divisor by the quotient obtained from the division step.

Write the result beneath the dividend, aligning it with the appropriate place value.

Example: Divide 735 by 5

Step 3: Subtract

Subtract the result obtained from the multiplication step from the portion of the dividend you’ve worked with so far.

Write the difference below the line.

Example: Divide 735 by 5

Step 4: Bring Down

If there are still digits remaining in the dividend, bring down the next digit and append it to the result of the subtraction.

This creates a new number to work with.

Example: 

Step 5: Repeat

Repeat steps 2 through 4 until you’ve brought down all the digits of the dividend and there’s no remainder.

Example:

Quotient = 147

Examples of Long Division

To truly master how to do long division, it’s helpful to work through a variety of examples. Below are seven examples that cover different cases of long division, each with detailed steps and final calculations.

Example 1: Simple Division with No Remainder

Question: Divide 84 by 4.

Steps to Solve:

1. Divide the first digit: 8 ÷ 4 = 2.
2. Multiply: 2 × 4 = 8.
3. Subtract: 8 – 8 = 0.
4. Bring down the next digit: 4.
5. Divide: 4 ÷ 4 = 1.
6. Multiply: 1 × 4 = 4.
7. Subtract: 4 – 4 = 0.

Example 2:  Division with a Remainder

Question: Divide 29 by 5.

Steps to Solve:

1. Divide the first digit: 2 ÷ 5 = 0 (since 2 is less than 5, we consider the first two digits).
2. Divide: 29 ÷ 5 = 5.
3. Multiply: 5 × 5 = 25.
4. Subtract: 29 – 25 = 4.

Example 3: Division Requiring Multiple Bring Downs

Question: Divide 1234 by 6.

Steps:

1. Divide the first digit: 1 ÷ 6 = 0 (consider the first two digits).
2. Divide: 12 ÷ 6 = 2.
3. Multiply: 2 × 6 = 12.
4. Subtract: 12 – 12 = 0.
5. Bring down the next digit: 3.
6. Divide: 3 ÷ 6 = 0 (bring down the next digit).
7. Divide: 34 ÷ 6 = 5.
8. Multiply: 5 × 6 = 30.
9. Subtract: 34 – 30 = 4.

Example 4: Division with Larger Numbers

Question: Divide 9876 by 12.

Steps:

1. Divide the first two digits: 98 ÷ 12 = 8.
2. Multiply: 8 × 12 = 96.
3. Subtract: 98 – 96 = 2.
4. Bring down the next digit: 7.
5. Divide: 27 ÷ 12 = 2.
6. Multiply: 2 × 12 = 24.
7. Subtract: 27 – 24 = 3.
8. Bring down the next digit: 6.
9. Divide: 36 ÷ 12 = 3.
10. Multiply: 3 × 12 = 36.
11. Subtract: 36 – 36 = 0.

Example 5: Division Resulting in a Decimal

Question: Divide 22 by 7.

Steps:

1. Divide the first digit: 2 ÷ 7 = 0 (consider the first two digits).
2. Divide: 22 ÷ 7 = 3.
3. Multiply: 3 × 7 = 21.
4. Subtract: 22 – 21 = 1.
5. Add decimal and bring down 0: 10 ÷ 7 = 1.
6. Multiply: 1 × 7 = 7.
7. Subtract: 10 – 7 = 3.
8. Bring down 0: 30 ÷ 7 = 4.
9. Multiply: 4 × 7 = 28.
10. Subtract: 30 – 28 = 2.
11. Continue as needed for more decimal places.

Example 6: Division with Zeros in the Quotient

Question: Divide 2050 by 5.

Steps:

1. Divide the first digit: 2 ÷ 5 = 0 (consider the first two digits).
2. Divide: 20 ÷ 5 = 4.
3. Multiply: 4 × 5 = 20.
4. Subtract: 20 – 20 = 0.
5. Bring down the next digit: 5.
6. Divide: 5 ÷ 5 = 1.
7. Multiply: 1 × 5 = 5.
8. Subtract: 5 – 5 = 0.
9. Bring down the next digit: 0.
10. Divide: 0 ÷ 5 = 0.

Example 7: Long Division by a 2-Digit Number

Question: Divide 15432 by 32.

Steps:

1. Setup: Write 15432 (dividend) inside the division bracket and 32 (divisor) outside.
2. Divide the first portion: Look at the first two digits of the dividend (15). Since 15 is less than 32, consider the first three digits (154). Determine how many times 32 fits into 154.
3. 154 ÷ 32 ≈ 4 (since 32 × 4 = 128 and 32 × 5 = 160, which is too high).
4. Multiply: Multiply 4 by 32 to get 128.
5. Subtract: Subtract 128 from 154 to get the remainder (26).
6. Bring down the next digit: Bring down the next digit from the dividend, which is 3, making the new number 263.
7. Divide again: Determine how many times 32 fits into 263.
8. 263 ÷ 32 ≈ 8 (since 32 × 8 = 256 and 32 × 9 = 288, which is too high).
9. Multiply: Multiply 8 by 32 to get 256.
10. Subtract: Subtract 256 from 263 to get the remainder (7).
11. Bring down the next digit: Bring down the next digit from the dividend, which is 2, making the new number 72.
12. Divide again: Determine how many times 32 fits into 72.
13. 72 ÷ 32 ≈ 2 (since 32 × 2 = 64 and 32 × 3 = 96, which is too high).
14. Multiply: Multiply 2 by 32 to get 64.
15. Subtract: Subtract 64 from 72 to get the remainder (8).

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FAQs: How to Do Long Division

Q1. How to check the result of long division?

Multiply the quotient by the divisor and add the remainder. The result should match the original dividend.

Q2. How to handle zeros in long division?

If you encounter a zero in the dividend, bring it down as usual and continue the division process.

Q3. What if the dividend has fewer digits than the divisor?

The quotient will be a decimal or a fraction, with the entire dividend as the remainder if it cannot be divided.

Conclusion

In this article, we’ve explained how to do long division by defining it, providing a step-by-step guide, and offering practical examples. Mastering long division is important for boosting your math skills and confidence. For more help, WuKong Math is a great resource. They offer live, interactive classes and lots of learning materials that make math fun and effective. Whether you want to improve your grades or get ready for competitions, WuKong Math can help you reach your goals in mathematics.