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What is Division Without a Remainder (Exact Division)?
Grade Level:
Class 3
Maths, Computing, AI
Definition
What is it?
Division without a remainder, also called Exact Division, is when a number can be divided into equal parts with nothing left over. It means the divisor fits perfectly into the dividend a certain number of times. The remainder in such a division is always zero.
Simple Example
Quick Example
Imagine you have 15 ladoos and you want to share them equally among 3 friends. If each friend gets 5 ladoos, and no ladoos are left over, then this is an example of exact division. Everyone gets an equal share, and nothing is wasted!
Worked Example
Step-by-Step
Let's divide 24 by 4.
1. **Identify the numbers:** The dividend is 24 (the number being divided). The divisor is 4 (the number dividing).
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2. **Think of multiplication:** Ask yourself, 'What number multiplied by 4 gives me 24?'
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3. **Find the quotient:** We know that 4 x 6 = 24. So, 6 is the quotient.
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4. **Subtract:** Subtract 24 from 24 (24 - 24 = 0).
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5. **Check the remainder:** The remainder is 0.
So, 24 divided by 4 is 6, with no remainder. This is exact division.
Why It Matters
Understanding exact division is crucial for fields like Computing and AI, where data needs to be split evenly for processing. In careers like data analysis or software development, you'll often divide tasks or resources perfectly. It's the basic building block for more complex calculations.
Common Mistakes
MISTAKE: Confusing exact division with division that has a remainder. Forgetting to check if anything is left over. | CORRECTION: Always check if the remainder is zero. If it's not zero, it's not exact division.
MISTAKE: Not knowing multiplication tables well, leading to incorrect quotients. | CORRECTION: Practice your multiplication tables regularly. A strong grasp of multiplication makes exact division much easier and faster.
MISTAKE: Thinking that any division results in a whole number quotient. | CORRECTION: Only exact division results in a whole number quotient with no remainder. Other divisions might result in fractions or decimals.
Practice Questions
Try It Yourself
QUESTION: A class has 30 students. If they are divided into 5 equal groups for a project, how many students will be in each group? Is this exact division? | ANSWER: 6 students per group. Yes, it is exact division.
QUESTION: You have 42 rupees and want to buy pencils that cost 6 rupees each. How many pencils can you buy exactly? | ANSWER: 7 pencils.
QUESTION: An auto-rickshaw driver covered 72 km in 3 hours. If he covered an equal distance each hour, how many kilometers did he cover in one hour? Is there any remainder? | ANSWER: 24 km per hour. No remainder.
MCQ
Quick Quiz
Which of the following is an example of exact division?
10 divided by 3
16 divided by 5
25 divided by 4
36 divided by 6
The Correct Answer Is:
D
36 divided by 6 equals 6, with a remainder of 0. All other options (10/3, 16/5, 25/4) result in a remainder, meaning they are not exact divisions.
Real World Connection
In the Real World
When you use a mobile app like 'Splitwise' to divide a dinner bill equally among friends, you're using exact division if the total amount divides perfectly. Or, when a school distributes 120 textbooks equally among 10 classes, it's exact division if each class gets 12 books with none left over.
Key Vocabulary
Key Terms
DIVIDEND: The number being divided | DIVISOR: The number by which another number is divided | QUOTIENT: The result of division | REMAINDER: The amount left over after division | EXACT DIVISION: Division where the remainder is zero
What's Next
What to Learn Next
Great job understanding exact division! Next, you should explore 'Division with a Remainder'. This will help you understand what happens when numbers don't divide perfectly, which is also very common in daily life and maths problems.
