What is The Concept of Remainder?

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Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

The remainder is the number left over after dividing one number by another. It tells us how much is 'extra' or 'not fitting' perfectly into equal groups after a division.

Simple Example

Quick Example

Imagine you have 10 laddoos and want to share them equally among 3 friends. Each friend gets 3 laddoos, but 1 laddoo is left over. This 1 laddoo is the remainder.

Worked Example

Step-by-Step

Let's divide 17 by 5 to find the remainder.

Step 1: Think how many times 5 can fit into 17 without going over. 5 x 1 = 5, 5 x 2 = 10, 5 x 3 = 15, 5 x 4 = 20 (too much).
---Step 2: So, 5 fits into 17 exactly 3 times (since 5 x 3 = 15).
---Step 3: Now, subtract this product from the original number: 17 - 15 = 2.
---Step 4: The number left, which is 2, is our remainder.

Answer: When 17 is divided by 5, the remainder is 2.

Why It Matters

Understanding remainders is crucial for solving many real-life problems, from sharing items fairly to managing inventory. It's used by software developers for coding, by engineers designing systems, and even by shopkeepers managing stock.

Common Mistakes

MISTAKE: Making the remainder larger than the divisor. | CORRECTION: The remainder must always be smaller than the number you are dividing by (the divisor). If it's larger, it means you can divide further.

MISTAKE: Confusing the quotient with the remainder. | CORRECTION: The quotient is how many full groups you can make (the result of the division), while the remainder is what's left over.

MISTAKE: Not performing the subtraction step correctly. | CORRECTION: After multiplying the divisor by the quotient, always subtract this product from the dividend to find the correct leftover amount.

Practice Questions

Try It Yourself

QUESTION: What is the remainder when 25 gulab jamuns are divided equally among 4 plates? | ANSWER: 1

QUESTION: A bus has a seating capacity of 30 people. If 100 passengers need to travel, how many passengers will be left after the bus makes full trips? (This is the remainder). | ANSWER: 10

QUESTION: A shopkeeper has 58 packets of biscuits. If each carton can hold 9 packets, how many full cartons can he make, and how many packets will be left unpackaged? | ANSWER: 6 full cartons, 4 packets left (remainder is 4)

MCQ

Quick Quiz

What is the remainder when 40 is divided by 6?

The Correct Answer Is:

6 goes into 40 six times (6 x 6 = 36). When you subtract 36 from 40, you are left with 4. So, the remainder is 4.

Real World Connection

In the Real World

When you buy mobile data packs, if you have 2GB data and use 500MB each day, the remainder tells you how much data is left. Or, when a delivery app like Swiggy or Zomato calculates how many delivery cycles are needed for multiple orders, they use remainders to figure out extra orders that need a separate trip.

Key Vocabulary

Key Terms

REMAINDER: The number left over after division | DIVIDEND: The number being divided | DIVISOR: The number by which another number is divided | QUOTIENT: The result of a division (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'. Knowing remainders will help you understand why certain numbers are perfectly divisible by others and make calculations even faster.