Checking Division (Dividend = Divisor × Quotient + Remainder)
When you divide a number, how do you know your answer is correct? There is a simple check formula that connects the four parts of every division: the dividend, divisor, quotient, and remainder.
In Class 4, you will learn to verify any division answer using this relationship. This skill helps you catch mistakes in long division and builds confidence in your calculations.
What is Checking Division - Class 4 Maths (Division)?
In any division:
- Dividend — the number being divided
- Divisor — the number you divide by
- Quotient — the answer (how many times the divisor fits)
- Remainder — what is left over
The division check formula states:
Dividend = (Divisor × Quotient) + Remainder
If this equation holds true, your division is correct. The remainder must always be less than the divisor.
Checking Division (Dividend = Divisor × Quotient + Remainder) Formula
Dividend = Divisor × Quotient + Remainder
Conditions:
- Remainder must be 0 or positive, and always less than the divisor.
- If the remainder is 0, then Dividend = Divisor × Quotient (exact division).
Solved Examples
Example 1: Example 1: Basic check with remainder
Problem: 47 ÷ 6 gives Quotient = 7, Remainder = 5. Check the answer.
Solution:
Step 1: Dividend = Divisor × Quotient + Remainder
Step 2: = 6 × 7 + 5 = 42 + 5 = 47
Step 3: 47 = 47 ✓ and Remainder (5) < Divisor (6) ✓
Answer: The division is correct.
Example 2: Example 2: Exact division (remainder = 0)
Problem: 72 ÷ 8 gives Quotient = 9, Remainder = 0. Check the answer.
Solution:
Step 1: Dividend = 8 × 9 + 0 = 72 + 0 = 72
Step 2: 72 = 72 ✓
Answer: The division is correct. Since the remainder is 0, 72 is exactly divisible by 8.
Example 3: Example 3: Finding a wrong answer
Problem: Aman says 85 ÷ 9 = 8 remainder 13. Is he correct?
Solution:
Step 1: Check: 9 × 8 + 13 = 72 + 13 = 85 ✓ (sum matches)
Step 2: But Remainder (13) > Divisor (9) ✗
Step 3: The remainder must be less than the divisor. The correct answer is 85 ÷ 9 = 9 remainder 4.
Step 4: Verify: 9 × 9 + 4 = 81 + 4 = 85 ✓ and 4 < 9 ✓
Answer: Aman's answer is wrong. The correct quotient is 9 and remainder is 4.
Example 4: Example 4: Word problem — sharing equally
Problem: Priya has 157 stickers to distribute equally among 12 friends. How many stickers does each friend get? How many are left? Check your answer.
Solution:
Step 1: 157 ÷ 12 → Quotient = 13, Remainder = 1
Step 2: Check: 12 × 13 + 1 = 156 + 1 = 157 ✓
Step 3: Remainder (1) < Divisor (12) ✓
Answer: Each friend gets 13 stickers, and 1 sticker is left over.
Example 5: Example 5: Finding the dividend
Problem: Divisor = 15, Quotient = 8, Remainder = 7. Find the dividend.
Solution:
Step 1: Dividend = Divisor × Quotient + Remainder
Step 2: Dividend = 15 × 8 + 7 = 120 + 7 = 127
Answer: The dividend is 127.
Example 6: Example 6: Finding the divisor
Problem: Dividend = 93, Quotient = 11, Remainder = 5. Find the divisor.
Solution:
Step 1: Dividend = Divisor × Quotient + Remainder
Step 2: 93 = Divisor × 11 + 5
Step 3: 93 − 5 = Divisor × 11
Step 4: 88 = Divisor × 11
Step 5: Divisor = 88 ÷ 11 = 8
Answer: The divisor is 8.
Example 7: Example 7: Finding the remainder
Problem: Dividend = 200, Divisor = 13, Quotient = 15. Find the remainder.
Solution:
Step 1: Dividend = Divisor × Quotient + Remainder
Step 2: 200 = 13 × 15 + Remainder
Step 3: 200 = 195 + Remainder
Step 4: Remainder = 200 − 195 = 5
Step 5: Check: 5 < 13 ✓
Answer: The remainder is 5.
Example 8: Example 8: Large number division check
Problem: 1,458 ÷ 25 gives Quotient = 58, Remainder = 8. Verify.
Solution:
Step 1: 25 × 58 + 8
Step 2: 25 × 58 = 1,450
Step 3: 1,450 + 8 = 1,458 ✓
Step 4: Remainder (8) < Divisor (25) ✓
Answer: The division is correct.
Example 9: Example 9: Finding the quotient
Problem: Dividend = 365, Divisor = 7, Remainder = 1. Find the quotient.
Solution:
Step 1: 365 = 7 × Quotient + 1
Step 2: 365 − 1 = 7 × Quotient
Step 3: 364 = 7 × Quotient
Step 4: Quotient = 364 ÷ 7 = 52
Answer: The quotient is 52.
Example 10: Example 10: Cricket ball word problem
Problem: A school ordered 500 cricket balls. They are packed in boxes of 12. How many full boxes are there? How many balls are left? Verify your answer.
Solution:
Step 1: 500 ÷ 12 → Quotient = 41, Remainder = 8
Step 2: Check: 12 × 41 + 8 = 492 + 8 = 500 ✓
Answer: There are 41 full boxes and 8 balls left over.
Key Points to Remember
- Division check formula: Dividend = Divisor × Quotient + Remainder.
- The remainder must always be less than the divisor. If it is not, the quotient is too small.
- When the remainder is 0, the division is exact (no leftover).
- You can use this formula to find any missing part — dividend, divisor, quotient, or remainder.
- Always verify long division answers using this check.
- The four parts of division are: Dividend, Divisor, Quotient, Remainder.
Practice Problems
- Divide 83 by 9. Write the quotient and remainder. Verify using the check formula.
- Dividend = 245, Divisor = 6, Quotient = 40, Remainder = 5. Is this division correct?
- Find the dividend if Divisor = 14, Quotient = 12, Remainder = 9.
- Dev says 100 ÷ 7 = 15 remainder 5. Check if he is correct.
- Ria divides a number by 8 and gets quotient 23 and remainder 3. What number did she divide?
- 567 ÷ 20 = Quotient 28, Remainder 7. Verify.
- Find the remainder when 999 is divided by 13. Verify your answer.
Frequently Asked Questions
Q1. What is the formula to check division?
Dividend = Divisor × Quotient + Remainder. If both sides are equal and the remainder is less than the divisor, the division is correct.
Q2. What happens when the remainder is 0?
When the remainder is 0, the dividend is exactly divisible by the divisor. The formula becomes Dividend = Divisor × Quotient.
Q3. Can the remainder be larger than the divisor?
No. If the remainder is larger than or equal to the divisor, the quotient is too small. You need to increase the quotient and recalculate.
Q4. How do you find the dividend using the check formula?
Multiply the divisor by the quotient, then add the remainder. Dividend = Divisor × Quotient + Remainder.
Q5. How do you find the divisor if the other three parts are known?
Subtract the remainder from the dividend, then divide by the quotient. Divisor = (Dividend − Remainder) ÷ Quotient.
Q6. Why is checking division important?
Long division involves many steps and small mistakes are common. The check formula lets you verify your answer quickly without redoing the entire division.
Q7. What are the four parts of a division?
The four parts are the dividend (number being divided), divisor (number you divide by), quotient (the answer), and remainder (what is left over).
Q8. Can this formula be used for large numbers?
Yes. The formula Dividend = Divisor × Quotient + Remainder works for all whole numbers, no matter how large. It is especially useful for checking long division with 4-digit or 5-digit dividends.
