# 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 skil

l. 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:

**Dividend:**This represents the number being divided. It is the larger number in the division problem and is divided by the divisor.**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.**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.**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:**

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

**Example 2: Division with a Remainder**

**Question: **Divide 29 by 5.

**Steps to Solve:**

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

**Example 3: Division Requiring Multiple Bring Downs**

**Question: **Divide 1234 by 6.

**Steps:**

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

**Example 4: Division with Larger Numbers**

**Question: **Divide 9876 by 12.

**Steps:**

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

**Example 5: Division Resulting in a Decimal**

**Question: **Divide 22 by 7.

**Steps:**

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

**Example 6: Division with Zeros in the Quotient**

**Question:** Divide 2050 by 5.

**Steps:**

- Divide the first digit: 2 ÷ 5 = 0 (consider the first two digits).
- Divide: 20 ÷ 5 = 4.
- Multiply: 4 × 5 = 20.
- Subtract: 20 – 20 = 0.
- Bring down the next digit: 5.
- Divide: 5 ÷ 5 = 1.
- Multiply: 1 × 5 = 5.
- Subtract: 5 – 5 = 0.
- Bring down the next digit: 0.
- Divide: 0 ÷ 5 = 0.

**Example 7: Long Division by a 2-Digit Number**

**Question: **Divide 15432 by 32.

**Steps:**

- Setup: Write 15432 (dividend) inside the division bracket and 32 (divisor) outside.
- 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.
- 154 ÷ 32 ≈ 4 (since 32 × 4 = 128 and 32 × 5 = 160, which is too high).
- Multiply: Multiply 4 by 32 to get 128.
- Subtract: Subtract 128 from 154 to get the remainder (26).
- Bring down the next digit: Bring down the next digit from the dividend, which is 3, making the new number 263.
- Divide again: Determine how many times 32 fits into 263.
- 263 ÷ 32 ≈ 8 (since 32 × 8 = 256 and 32 × 9 = 288, which is too high).
- Multiply: Multiply 8 by 32 to get 256.
- Subtract: Subtract 256 from 263 to get the remainder (7).
- Bring down the next digit: Bring down the next digit from the dividend, which is 2, making the new number 72.
- Divide again: Determine how many times 32 fits into 72.
- 72 ÷ 32 ≈ 2 (since 32 × 2 = 64 and 32 × 3 = 96, which is too high).
- Multiply: Multiply 2 by 32 to get 64.
- Subtract: Subtract 64 from 72 to get the remainder (8).

**Introducing ****WuKong Math****: Unleashing the Math Whiz in Every Child**

When it comes to learning long division and other essential math skills, WuKong Math offers a stellar educational experience that helps students excel. Designed for students from grades 1 to 12, WuKong Math provides live, interactive classes that make math enjoyable and engaging. Here’s why WuKong Math stands out as an excellent resource for mastering long division and enhancing overall math proficiency.

**Course Highlights:**

**Global Accessibility:**WuKong Math is available in all 24 global time zones, making it suitable for students worldwide.**Live Instruction:**Students benefit from live math classes taught by experienced instructors who are experts in igniting a love for math.- Interactive Sessions: The blended learning approach includes small-group sessions online, fostering interactive and personalized learning experiences.
**Structured Curriculum:**WuKong’s courses are copyrighted and come with a clear grading system to track progress and ensure understanding.**Qualified Instructors:**Their team of teachers spans the United States, Singapore, Australia, the United Kingdom, and more. These instructors are graduates from world-renowned universities and bring practical knowledge and experience in mathematics education.**Extensive****Math Resources****:**WuKong provides access to hundreds of original math learning resources, ensuring students have plenty of materials to practice and enhance their skills.

**Course Benefits:**

**Enhanced Learning:**WuKong Math’s courses are designed to boost mathematical thinking skills and improve math grades through well-structured lessons and interactive learning.**Competition Preparation:**For students aiming to compete internationally, WuKong offers advanced enrichment courses tailored to various math competitions, equipping them with the confidence and skills needed to excel.**Comprehensive Coverage:**With 10 levels of advanced courses, WuKong accommodates students of different countries, grades, and learning backgrounds, ensuring each student finds courses that match their learning needs.**Innovative Teaching Methods:**WuKong incorporates Singapore’s CPA modeling teaching approach, which uses graphics for mathematical modeling to help students transition from concrete to abstract thinking. This method fosters creative problem-solving skills.

**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.

Discovering the maths whiz in every child,

that’s what we do.

Suitable for students worldwide, from grades 1 to 12.

Get started free!Delvair holds a degree in Physics from the Federal University of Maranhão, Brazil. With over six years of experience, she specializes in teaching mathematics, with a particular emphasis on Math Kangaroo competitions. She firmly believes that education is the cornerstone of society’s future. Additionally, she holds the conviction that every child can learn given the right environment and guidance. In her spare time, she enjoys singing and tending to her plants.