Division With Remainder (Grade 4)
Division with remainder occurs when a number cannot be divided exactly by another number. The leftover part after dividing is called the remainder.
In Class 4, understanding remainders is important for solving real-life problems like sharing items when they do not split evenly, or finding how many complete groups can be formed.
What is Division With Remainder (Grade 4) - Class 4 Maths (Division (Grade 4))?
When a dividend is divided by a divisor and the division is not exact, we get a quotient (the number of complete groups) and a remainder (the leftover amount).
Dividend = Divisor × Quotient + Remainder
Key rule: The remainder is always less than the divisor (0 ≤ Remainder < Divisor).
Types and Properties
Different situations involving remainders:
- Remainder = 0: Exact division. Example: 24 ÷ 6 = 4 R 0.
- Remainder > 0: Not exact. Example: 25 ÷ 6 = 4 R 1.
- Interpreting the remainder: In word problems, the remainder may mean:
- Extra items left over (ignore the remainder)
- Need one more group (round up the quotient)
- The remainder itself is the answer
Solved Examples
Example 1: Example 1: Basic Division with Remainder
Problem: Divide 29 ÷ 4
Solution:
4 × 7 = 28 (closest to 29 without exceeding)
Remainder = 29 − 28 = 1
Answer: 29 ÷ 4 = 7 remainder 1
Check: 4 × 7 + 1 = 28 + 1 = 29 ✓
Example 2: Example 2: 3-Digit Division with Remainder
Problem: Divide 547 ÷ 6
Solution:
54 ÷ 6 = 9 (6 × 9 = 54). Subtract: 54 − 54 = 0.
Bring down 7. 7 ÷ 6 = 1 (6 × 1 = 6). Subtract: 7 − 6 = 1.
Answer: 547 ÷ 6 = 91 remainder 1
Check: 6 × 91 + 1 = 546 + 1 = 547 ✓
Example 3: Example 3: Sharing (Remainder Means Leftover)
Problem: Ria has 43 toffees. She shares them equally among 5 friends. How many does each friend get? How many are left?
Solution:
43 ÷ 5 = 8 remainder 3 (5 × 8 = 40; 43 − 40 = 3)
Answer: Each friend gets 8 toffees. 3 toffees are left with Ria.
Example 4: Example 4: Grouping (Round Up the Quotient)
Problem: A bus holds 9 students. There are 50 students going on a trip. How many buses are needed?
Solution:
50 ÷ 9 = 5 remainder 5
5 buses carry 45 students. The remaining 5 students still need a bus.
Answer: 6 buses are needed. (We round UP because every student must have a seat.)
Example 5: Example 5: Remainder Is the Answer
Problem: Meera has ₹75. She buys as many notebooks as she can at ₹8 each. How much money does she have left?
Solution:
75 ÷ 8 = 9 remainder 3 (8 × 9 = 72; 75 − 72 = 3)
She buys 9 notebooks. The question asks how much is LEFT.
Answer: Meera has ₹3 left.
Example 6: Example 6: Finding the Largest Possible Remainder
Problem: What is the largest possible remainder when dividing by 7?
Solution:
The remainder must be less than the divisor.
Largest remainder = 7 − 1 = 6
Example: 48 ÷ 7 = 6 remainder 6 (7 × 6 = 42; 48 − 42 = 6)
Answer: The largest possible remainder is 6.
Example 7: Example 7: Checking Division
Problem: Arjun says 185 ÷ 6 = 31 remainder 1. Is he correct?
Solution:
Check: 6 × 31 + 1 = 186 + 1 = 187
But the dividend is 185, not 187. So Arjun is wrong.
Correct: 6 × 30 + 5 = 180 + 5 = 185. So 185 ÷ 6 = 30 remainder 5.
Answer: Arjun is incorrect. The correct answer is 30 remainder 5.
Example 8: Example 8: Finding the Dividend
Problem: When a number is divided by 8, the quotient is 12 and the remainder is 5. Find the number.
Solution:
Dividend = Divisor × Quotient + Remainder
Dividend = 8 × 12 + 5 = 96 + 5 = 101
Answer: The number is 101.
Example 9: Example 9: Packing Problem
Problem: Aditi has 200 beads. She packs them into bags of 9. How many full bags does she get? How many beads are unpacked?
Solution:
200 ÷ 9 = 22 remainder 2 (9 × 22 = 198; 200 − 198 = 2)
Answer: Aditi gets 22 full bags with 2 beads unpacked.
Example 10: Example 10: Pattern of Remainders
Problem: Find the remainders when 10, 11, 12, 13, 14, 15 are divided by 3. What pattern do you see?
Solution:
| Dividend | ÷ 3 | Quotient | Remainder |
|---|---|---|---|
| 10 | ÷ 3 | 3 | 1 |
| 11 | ÷ 3 | 3 | 2 |
| 12 | ÷ 3 | 4 | 0 |
| 13 | ÷ 3 | 4 | 1 |
| 14 | ÷ 3 | 4 | 2 |
| 15 | ÷ 3 | 5 | 0 |
Answer: The remainders follow a repeating pattern: 1, 2, 0, 1, 2, 0.
Real-World Applications
Division with remainder is used in everyday situations:
- Sharing food: 23 chapatis among 4 people — each gets 5, 3 are left.
- Seating: 50 students in rows of 8 — 6 rows full, 2 students need a 7th row.
- Money: Finding how many items you can buy and how much money remains.
- Packing: How many full boxes and how many items are unpacked.
Key Points to Remember
- The remainder is the amount left over after division.
- The remainder is always less than the divisor.
- Check formula: Dividend = Divisor × Quotient + Remainder.
- In word problems, interpret the remainder based on the situation:
- Left over → the remainder is extra items
- Need one more group → add 1 to the quotient
- The remainder itself is the answer
- If the remainder equals 0, the division is exact.
- The largest possible remainder = divisor − 1.
Practice Problems
- Find the quotient and remainder: 67 ÷ 5.
- Divide 345 ÷ 7 and check your answer.
- Kavi has 100 pencils. She ties them in bundles of 6. How many bundles and how many pencils are left?
- What is the largest remainder you can get when dividing by 9?
- A number divided by 5 gives quotient 24 and remainder 3. Find the number.
- Dev has ₹150. He buys cricket balls at ₹18 each. How many can he buy? How much money is left?
- Is 432 exactly divisible by 6? How do you know?
- 53 students sit in rows of 7. How many rows are needed? (Think carefully about the remainder!)
Frequently Asked Questions
Q1. What does remainder mean in division?
The remainder is the amount left over when a number cannot be divided exactly. For example, when 17 is divided by 5, 3 groups of 5 make 15, and 2 is left over. So the remainder is 2.
Q2. Can the remainder be greater than the divisor?
No. If the remainder is greater than or equal to the divisor, the quotient should be increased. The remainder must always be less than the divisor.
Q3. How do I check if my division with remainder is correct?
Multiply the quotient by the divisor and add the remainder. If you get the original dividend, the answer is correct. For example: 47 ÷ 5 = 9 R 2. Check: 5 × 9 + 2 = 47.
Q4. When should I round up the quotient in a word problem?
Round up when everyone or everything must be included. For example, if 50 students need buses that hold 9 each, you need 6 buses (not 5), because the 5 remaining students also need a bus.
Q5. What if the remainder is 0?
A remainder of 0 means the division is exact — the divisor divides the dividend perfectly. For example, 36 ÷ 6 = 6 remainder 0.
Q6. What is the smallest and largest possible remainder when dividing by 4?
The smallest possible remainder is 0 (exact division). The largest possible remainder is 3 (one less than the divisor 4).
Q7. How do I find the dividend if I know the quotient, divisor, and remainder?
Use the formula: Dividend = Divisor × Quotient + Remainder. For example, if divisor = 7, quotient = 15, remainder = 3, then dividend = 7 × 15 + 3 = 108.
Q8. Is division with remainder in the NCERT Class 4 syllabus?
Yes. NCERT Class 4 Maths covers division with remainder and emphasises checking division using the relationship between dividend, divisor, quotient, and remainder.
Q9. Do remainders form a pattern?
Yes. When consecutive numbers are divided by the same divisor, the remainders cycle through 0, 1, 2, ..., (divisor − 1) in a repeating pattern.
