What is Long Division?

S1-SA1-0136

Grade Level:

Class 5

Maths, Computing, AI, Algorithms

Definition

What is it?

Long division is a method used to divide large numbers into smaller groups or parts. It helps us find out how many times one number (the divisor) fits into another number (the dividend) and what's left over (the remainder). It breaks down a big division problem into several easier steps.

Simple Example

Quick Example

Imagine you have 125 ladoos to distribute equally among 5 friends. How many ladoos does each friend get? Long division helps you figure out that each friend gets 25 ladoos, with no ladoos left over.

Worked Example

Step-by-Step

Let's divide 735 by 5.

Step 1: Write the problem. Divisor (5) outside, Dividend (735) inside.
5 | 735

---
Step 2: Divide the first digit of the dividend (7) by the divisor (5). 5 goes into 7 one time (1 x 5 = 5).
1
5 | 735
-5
---
2

---
Step 3: Bring down the next digit (3) to make 23. Divide 23 by 5. 5 goes into 23 four times (4 x 5 = 20).
14
5 | 735
-5
---
23
-20
---
3

---
Step 4: Bring down the last digit (5) to make 35. Divide 35 by 5. 5 goes into 35 seven times (7 x 5 = 35).
147
5 | 735
-5
---
23
-20
---
35
-35
---
0

---
Answer: The quotient is 147 and the remainder is 0. So, 735 divided by 5 is 147.

Why It Matters

Long division is a basic algorithm, just like the steps a computer follows to solve a problem. It's crucial for understanding how computers perform calculations and process data. Engineers, data scientists, and even AI developers use these foundational ideas to build complex systems that manage everything from mobile networks to space missions.

Common Mistakes

MISTAKE: Forgetting to bring down the next digit | CORRECTION: Always remember to bring down the next digit of the dividend after each subtraction step to form the new number to divide.

MISTAKE: Incorrect multiplication during steps | CORRECTION: Double-check your multiplication facts. A small error here will lead to a completely wrong answer.

MISTAKE: Writing the remainder larger than the divisor | CORRECTION: The remainder must always be smaller than the divisor. If it's not, it means you could have divided at least one more time.

Practice Questions

Try It Yourself

QUESTION: Divide 567 by 3. | ANSWER: 189

QUESTION: Divide 892 by 4. | ANSWER: 223

QUESTION: A school has 675 students. If they are divided into groups of 15 for a sports event, how many groups will there be? | ANSWER: 45 groups

MCQ

Quick Quiz

When you divide 428 by 2 using long division, what is the quotient?

210

214

224

204

The Correct Answer Is:

To divide 428 by 2, first divide 4 by 2 to get 2. Then divide 2 by 2 to get 1. Finally, divide 8 by 2 to get 4. Putting these together gives 214.

Real World Connection

In the Real World

Long division helps in many daily tasks. For instance, if you're planning a road trip from Delhi to Jaipur (around 270 km) and your car covers 15 km per litre of petrol, long division helps you calculate exactly how many litres you need. Or, if a shopkeeper needs to divide a bulk order of 500 pencils equally into 25 boxes, long division tells them how many pencils go into each box.

Key Vocabulary

Key Terms

DIVIDEND: The number being divided | DIVISOR: The number by which another number is divided | QUOTIENT: The result obtained by dividing one number by another | REMAINDER: The amount left over after dividing one integer by another | ALGORITHM: A step-by-step procedure for solving a problem

What's Next

What to Learn Next

Great job understanding long division! Now that you know how to divide whole numbers, you're ready to explore 'Division with Decimals.' This will help you divide numbers that aren't perfectly whole, like splitting a bill for chai among friends.