What is a Remainder?

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Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

When we divide one number by another, sometimes a part is left over because it can't be divided equally. This leftover part is called the remainder. It's the amount that 'remains' after the division.

Simple Example

Quick Example

Imagine you have 7 ladoos and you want to share them equally among 3 friends. Each friend gets 2 ladoos (3 x 2 = 6 ladoos distributed). You are left with 1 ladoo that cannot be shared equally. That 1 ladoo is the remainder.

Worked Example

Step-by-Step

Let's divide 15 by 4.

Step 1: Think about how many times 4 can fit into 15 without going over.

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Step 2: If we multiply 4 by 1, we get 4. (Too small)

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Step 3: If we multiply 4 by 2, we get 8. (Still too small)

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Step 4: If we multiply 4 by 3, we get 12. (This is the closest we can get without going over 15)

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Step 5: If we multiply 4 by 4, we get 16. (This is too big, it's more than 15)

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Step 6: So, 4 goes into 15 three times (3 is the quotient).

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Step 7: Now, subtract 12 (4 x 3) from 15. 15 - 12 = 3.

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Step 8: The number left over is 3. This is our remainder.

Answer: When 15 is divided by 4, the remainder is 3.

Why It Matters

Understanding remainders helps you solve problems where things don't divide perfectly. It's useful in computer programming for checking even/odd numbers, in logistics for packing items efficiently, and even in designing calendars. Engineers and data scientists use this concept often.

Common Mistakes

MISTAKE: Thinking the remainder can be larger than the divisor. For example, saying the remainder of 10 divided by 3 is 4. | CORRECTION: The remainder must always be smaller than the divisor. If your remainder is larger, it means you could have divided at least one more time.

MISTAKE: Confusing the quotient with the remainder. For example, in 10 divided by 3, saying the remainder is 3 (which is the quotient). | CORRECTION: The quotient is how many times the divisor fits into the number. The remainder is what's left over after that full division.

MISTAKE: Forgetting to subtract the product of the quotient and divisor from the original number. For example, just guessing the remainder without calculation. | CORRECTION: Always calculate (divisor x quotient) and subtract it from the dividend to find the exact remainder.

Practice Questions

Try It Yourself

QUESTION: What is the remainder when 20 is divided by 6? | ANSWER: 2

QUESTION: A tailor has 35 buttons and needs to put 8 buttons on each shirt. How many buttons will be left over after making as many shirts as possible? | ANSWER: 3

QUESTION: If you have 50 rupees and buy samosas that cost 7 rupees each, what is the maximum number of samosas you can buy, and how much money will you have left? | ANSWER: You can buy 7 samosas, and you will have 1 rupee left.

MCQ

Quick Quiz

When 23 is divided by 5, what is the remainder?

The Correct Answer Is:

5 goes into 23 four times (5 x 4 = 20). When you subtract 20 from 23, you are left with 3. So, 3 is the remainder.

Real World Connection

In the Real World

Imagine a delivery driver for Swiggy or Zomato who has 25 food packets and needs to deliver them to areas where each delivery vehicle can carry 6 packets. To find out how many packets will be left for the last vehicle (or if an extra trip is needed), they use remainders. This helps in planning routes and vehicle usage efficiently.

Key Vocabulary

Key Terms

REMAINDER: The amount left over after a division when the numbers don't divide evenly. | DIVIDEND: The number being divided. | DIVISOR: The number by which another number is divided. | QUOTIENT: The result of a division, showing how many times the divisor fits into the dividend.

What's Next

What to Learn Next

Great job understanding remainders! Next, you can explore 'Divisibility Rules' to quickly tell if a number can be divided by another without a remainder. This will make your division calculations even faster and smarter!