Division With Remainder
Sometimes a number does not divide equally. There are some items left over after making equal groups. This leftover is called the remainder.
In Class 3, you learn to write division answers with a remainder and understand the rule that the remainder is always less than the divisor.
What is Division With Remainder - Class 3 Maths (Division)?
When the dividend is not an exact multiple of the divisor, the division has a remainder.
Dividend = (Divisor × Quotient) + Remainder
Example: 17 ÷ 5 → 5 × 3 = 15, leftover = 17 − 15 = 2. So 17 ÷ 5 = 3 remainder 2.
Rule: The remainder is always less than the divisor.
Solved Examples
Example 1: Simple Remainder
Question: Find 13 ÷ 4.
Think:
- 4 × 3 = 12 (closest without going over 13)
- Remainder = 13 − 12 = 1
Answer: 13 ÷ 4 = 3 remainder 1.
Example 2: Word Problem — Sharing Toffees
Question: Aman has 23 toffees and shares them equally among 5 friends. How many does each get? How many are left?
Think:
- 5 × 4 = 20
- Each friend gets 4 toffees.
- Left over = 23 − 20 = 3
Answer: Each friend gets 4 toffees, and 3 toffees are left.
Example 3: Remainder with Divisor 3
Question: Find 20 ÷ 3.
Think:
- 3 × 6 = 18 (closest to 20)
- Remainder = 20 − 18 = 2
Answer: 20 ÷ 3 = 6 remainder 2.
Example 4: Checking the Answer
Question: Verify that 29 ÷ 6 = 4 remainder 5.
Think:
- Check: (6 × 4) + 5 = 24 + 5 = 29 ✓
- Is remainder (5) less than divisor (6)? Yes ✓
Answer: The answer is correct.
Example 5: Word Problem — Packing Eggs
Question: Neha has 26 eggs. Each tray holds 6 eggs. How many full trays? How many eggs are left?
Think:
- 6 × 4 = 24
- Full trays = 4
- Left over = 26 − 24 = 2
Answer: 4 full trays and 2 eggs left.
Example 6: Remainder with Divisor 7
Question: Find 50 ÷ 7.
Think:
- 7 × 7 = 49 (closest to 50)
- Remainder = 50 − 49 = 1
Answer: 50 ÷ 7 = 7 remainder 1.
Example 7: Remainder = 0
Question: Find 24 ÷ 8.
Think:
- 8 × 3 = 24 (exact match)
- Remainder = 0
Answer: 24 ÷ 8 = 3 remainder 0 (or simply 3). When remainder is 0, the division is exact.
Example 8: Word Problem — Seating
Question: 34 students sit in rows of 8. How many full rows? How many students in the last row?
Think:
- 8 × 4 = 32
- Remaining students = 34 − 32 = 2
Answer: 4 full rows and 2 students in the last row.
Example 9: Finding Missing Dividend
Question: ___ ÷ 5 = 7 remainder 3. Find the dividend.
Think:
- Dividend = (Divisor × Quotient) + Remainder
- = (5 × 7) + 3 = 35 + 3 = 38
Answer: The dividend is 38.
Key Points to Remember
- A remainder is the amount left after dividing into equal groups.
- The remainder is always less than the divisor.
- Check formula: Dividend = (Divisor × Quotient) + Remainder.
- If the remainder is 0, the division is exact — no leftover.
- The largest possible remainder is one less than the divisor (e.g., dividing by 5 → largest remainder is 4).
- In word problems, the remainder tells you how many items are left over after equal sharing.
Practice Problems
- Find 19 ÷ 4. Write the quotient and remainder.
- Find 37 ÷ 6.
- Priya has 29 flowers. She makes bunches of 5. How many full bunches? How many flowers left?
- Check: Is 25 ÷ 7 = 3 remainder 4 correct?
- Find 43 ÷ 8.
- Dev has 31 marbles. He puts 9 in each bag. How many full bags? How many left?
- ___ ÷ 6 = 5 remainder 2. Find the dividend.
Frequently Asked Questions
Q1. What is a remainder in division?
It is the amount left over when a number cannot be divided into equal groups exactly. For example, 14 ÷ 3 = 4 remainder 2, because 3 × 4 = 12 and 14 − 12 = 2.
Q2. Can the remainder be larger than the divisor?
No. The remainder must always be less than the divisor. If it is equal to or larger, you need to increase the quotient.
Q3. What does remainder 0 mean?
It means the division is exact — there is nothing left over. For example, 18 ÷ 6 = 3 with no remainder.
Q4. How do I check a division with remainder?
Use the formula: Dividend = (Divisor × Quotient) + Remainder. If both sides are equal, your answer is correct.
Q5. What is the largest remainder when dividing by 5?
The largest possible remainder is 4, because the remainder must be less than the divisor (5).
Q6. How do I find the quotient in division with remainder?
Find the largest multiple of the divisor that is less than or equal to the dividend. The multiplier is the quotient. Subtract to find the remainder.
Q7. Can a remainder be negative?
No. In Class 3 division, the remainder is always 0 or a positive number less than the divisor.
Q8. Is division with remainder in the NCERT Class 3 syllabus?
Yes. NCERT Class 3 Maths teaches division with remainder through sharing, grouping, and word problems.
