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What is Remainder?
Grade Level:
Class 6
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
The remainder is the number left over when one number cannot be divided exactly by another. It tells us how much 'extra' there is after making equal groups.
Simple Example
Quick Example
Imagine you have 10 laddoos and you want to share them equally among 3 friends. Each friend gets 3 laddoos (3 x 3 = 9). You will have 1 laddoo left over. This 1 laddoo is the remainder.
Worked Example
Step-by-Step
Let's divide 17 by 5.
1. Start with the number 17 (dividend) and the number you are dividing by, 5 (divisor).
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2. Think: How many times can 5 go into 17 without going over?
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3. We know 5 x 1 = 5, 5 x 2 = 10, 5 x 3 = 15, and 5 x 4 = 20.
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4. Since 20 is greater than 17, we choose 5 x 3 = 15. So, the quotient is 3.
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5. Now, subtract this product from the original number: 17 - 15 = 2.
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6. The number left, 2, is the remainder.
So, when 17 is divided by 5, the quotient is 3 and the remainder is 2.
Why It Matters
Understanding remainders is super useful! It helps engineers design efficient computer programs and even helps scientists in physics calculate cycles. In data science, remainders are used in complex algorithms to sort information quickly, which can lead to new discoveries.
Common Mistakes
MISTAKE: Making the remainder larger than the divisor. For example, when dividing 10 by 3, saying the remainder is 4 (because 3x2=6, 10-6=4). | CORRECTION: The remainder must always be smaller than the divisor. If your remainder is larger, it means you could have divided more times.
MISTAKE: Forgetting about the remainder when the division isn't exact. For example, saying 13 divided by 4 is just 3. | CORRECTION: Always state the remainder if there is one. The correct answer for 13 divided by 4 is 3 with a remainder of 1.
MISTAKE: Confusing the quotient with the remainder. For example, when 7 is divided by 2, saying the remainder is 3. | CORRECTION: The quotient is how many times the divisor fits into the dividend (3 in this case). The remainder is what's left over (1 in this case).
Practice Questions
Try It Yourself
QUESTION: What is the remainder when 25 is divided by 4? | ANSWER: 1
QUESTION: A bus has seats for 8 passengers. If 30 students need to travel, how many students will be left behind after all full buses leave? | ANSWER: 6 students
QUESTION: You have 50 rupees and want to buy pens that cost 7 rupees each. How many pens can you buy, and how much money will be left over? | ANSWER: You can buy 7 pens, and 1 rupee will be left over.
MCQ
Quick Quiz
What is the remainder when 38 is divided by 6?
6
2
5
8
The Correct Answer Is:
B
When 38 is divided by 6, 6 goes into 38 six times (6 x 6 = 36). Subtracting 36 from 38 leaves 2. So, the remainder is 2.
Real World Connection
In the Real World
When you book train tickets online and want to know how many full groups of 4 can sit together in a coach, the remainder tells you how many people will be left over. Or, when a mobile app needs to show you 'x' number of items per page, it uses remainders to figure out how many items will be on the last, incomplete page.
Key Vocabulary
Key Terms
DIVIDEND: The number being divided | DIVISOR: The number by which another number is divided | QUOTIENT: The result of division, showing how many times the divisor fits | REMAINDER: The number left over after division
What's Next
What to Learn Next
Now that you understand remainders, you're ready to explore concepts like divisibility rules and factors and multiples. These build directly on remainders to help you understand how numbers relate to each other in even more exciting ways!
