Division of 4-Digit by 2-Digit Numbers
In Class 5, students learn to divide 4-digit numbers by 2-digit numbers using the long division method. This is one of the most important arithmetic skills, used for sharing things equally, calculating rates, and solving real-life problems involving distribution.
Long division with a 2-digit divisor requires careful estimation at each step. Students must judge how many times the divisor fits into different parts of the dividend, then multiply, subtract, and bring down the next digit.
What is Division of 4-Digit by 2-Digit Numbers - Class 5 Maths (Operations)?
Division is the process of splitting a number into equal groups. When dividing a 4-digit number (dividend) by a 2-digit number (divisor), we use the long division method.
Key terms:
- Dividend: The number being divided (e.g., 4,836)
- Divisor: The number we divide by (e.g., 12)
- Quotient: The result of division (e.g., 403)
- Remainder: The amount left over (e.g., 0)
Dividend = Divisor × Quotient + Remainder
Division of 4-Digit by 2-Digit Numbers Formula
Dividend ÷ Divisor = Quotient (Remainder R)
Steps of long division:
- Divide: How many times does the divisor go into the first group of digits?
- Multiply: Divisor × quotient digit.
- Subtract: Subtract the product from the current number.
- Bring down: Bring down the next digit of the dividend.
- Repeat steps 1-4 until all digits are used.
Solved Examples
Example 1: Example 1: Exact division
Problem: Divide 2,496 ÷ 12.
Solution:
Step 1: 12 goes into 24 → 2 times. 2 × 12 = 24. Subtract: 24 − 24 = 0.
Step 2: Bring down 9. 12 goes into 09 → 0 times. Write 0 in quotient. Bring down 6.
Step 3: 12 goes into 96 → 8 times. 8 × 12 = 96. Subtract: 96 − 96 = 0.
Answer: 2,496 ÷ 12 = 208
Example 2: Example 2: Division with remainder
Problem: Divide 3,457 ÷ 15.
Solution:
Step 1: 15 goes into 34 → 2 times. 2 × 15 = 30. Subtract: 34 − 30 = 4.
Step 2: Bring down 5. 15 goes into 45 → 3 times. 3 × 15 = 45. Subtract: 45 − 45 = 0.
Step 3: Bring down 7. 15 goes into 7 → 0 times. Write 0 in quotient.
Answer: 3,457 ÷ 15 = 230 remainder 7
Verification: 15 × 230 + 7 = 3,450 + 7 = 3,457 ✓
Example 3: Example 3: Larger divisor
Problem: Divide 5,278 ÷ 34.
Solution:
Step 1: 34 goes into 52 → 1 time. 1 × 34 = 34. Subtract: 52 − 34 = 18.
Step 2: Bring down 7. 34 goes into 187 → 5 times. 5 × 34 = 170. Subtract: 187 − 170 = 17.
Step 3: Bring down 8. 34 goes into 178 → 5 times. 5 × 34 = 170. Subtract: 178 − 170 = 8.
Answer: 5,278 ÷ 34 = 155 remainder 8
Example 4: Example 4: Division by a multiple of 10
Problem: Divide 7,200 ÷ 40.
Solution:
Shortcut: Cancel one zero from both dividend and divisor.
7,200 ÷ 40 = 720 ÷ 4 = 180
Answer: 7,200 ÷ 40 = 180
Example 5: Example 5: Word problem — Equal distribution
Problem: A school has 1,368 books to distribute equally among 24 classrooms. How many books does each classroom get?
Solution:
Step 1: 1,368 ÷ 24
Step 2: 24 goes into 136 → 5 times. 5 × 24 = 120. Subtract: 136 − 120 = 16.
Step 3: Bring down 8. 24 goes into 168 → 7 times. 7 × 24 = 168. Subtract: 168 − 168 = 0.
Answer: Each classroom gets 57 books.
Example 6: Example 6: Word problem — Rate calculation
Problem: Aman's father paid ₹4,950 for 18 kg of almonds. What is the price per kg?
Solution:
Price per kg = 4,950 ÷ 18
Step 1: 18 goes into 49 → 2 times. 2 × 18 = 36. Subtract: 49 − 36 = 13.
Step 2: Bring down 5. 18 goes into 135 → 7 times. 7 × 18 = 126. Subtract: 135 − 126 = 9.
Step 3: Bring down 0. 18 goes into 90 → 5 times. 5 × 18 = 90. Subtract: 90 − 90 = 0.
Answer: Price per kg = ₹275
Example 7: Example 7: Division where first pair is less than divisor
Problem: Divide 1,056 ÷ 32.
Solution:
Step 1: 32 goes into 10 → 0 times. Take the first 3 digits: 105.
Step 2: 32 goes into 105 → 3 times. 3 × 32 = 96. Subtract: 105 − 96 = 9.
Step 3: Bring down 6. 32 goes into 96 → 3 times. 3 × 32 = 96. Subtract: 96 − 96 = 0.
Answer: 1,056 ÷ 32 = 33
Example 8: Example 8: Verification using multiplication
Problem: Divide 8,645 ÷ 25 and verify the answer.
Solution:
8,645 ÷ 25 = 345 remainder 20
Verification: 25 × 345 + 20 = 8,625 + 20 = 8,645 ✓
Answer: Quotient = 345, Remainder = 20
Example 9: Example 9: Word problem — Seating arrangement
Problem: 2,700 students need to sit in rows of 45. How many rows are needed?
Solution:
2,700 ÷ 45 = 60
Shortcut: 2,700 ÷ 45 = 2,700 ÷ 9 ÷ 5 = 300 ÷ 5 = 60
Answer: 60 rows are needed.
Key Points to Remember
- Long division follows four steps: Divide, Multiply, Subtract, Bring down.
- The remainder must always be less than the divisor.
- To verify: Dividend = Divisor × Quotient + Remainder.
- If the first two digits of the dividend are less than the divisor, take the first three digits.
- When both dividend and divisor end in zero(s), cancel equal numbers of zeros to simplify.
- Estimation helps: round the divisor and use multiplication tables to guess each quotient digit.
- Practice multiplication tables up to 20 for faster long division with 2-digit divisors.
Practice Problems
- Divide 3,456 ÷ 16.
- Divide 5,832 ÷ 24.
- Divide 7,009 ÷ 37 and find the quotient and remainder.
- A farmer has 4,200 mangoes to pack in boxes of 35. How many boxes does he need?
- Divide 9,100 ÷ 50.
- Aditi scored 2,736 runs in 48 matches. What was her average score per match?
- Divide 6,543 ÷ 27. Verify your answer using multiplication.
- ₹8,400 is shared equally among 56 workers. How much does each worker get?
Frequently Asked Questions
Q1. What is long division?
Long division is a step-by-step method for dividing large numbers. You divide the digits of the dividend from left to right, multiplying and subtracting at each step, and bringing down the next digit until all digits are used.
Q2. How do I estimate the quotient digit?
Round the divisor to the nearest ten and use multiplication facts. For example, for 187 ÷ 34, think: 34 is close to 30, and 30 × 6 = 180. Try 5 or 6, then check by multiplying.
Q3. What if the remainder is larger than the divisor?
If the remainder is larger than or equal to the divisor, the quotient digit is too small. Increase the quotient digit by 1 and recalculate.
Q4. How do I verify my division answer?
Use the formula: Dividend = Divisor × Quotient + Remainder. Multiply the divisor by the quotient, add the remainder, and check if it equals the dividend.
Q5. When do I write 0 in the quotient?
Write 0 in the quotient when the divisor does not fit into the current number (the number is less than the divisor). Then bring down the next digit and continue.
Q6. Can I cancel zeroes to make division easier?
Yes. If both the dividend and divisor end in the same number of zeroes, you can cancel them. For example, 4,800 ÷ 60 = 480 ÷ 6 = 80.
Q7. What is the maximum number of digits the quotient can have?
When dividing a 4-digit number by a 2-digit number, the quotient has at most 3 digits (e.g., 9,999 ÷ 10 = 999) and at least 2 digits (e.g., 1,000 ÷ 99 = 10 remainder 10).
Q8. Why is division important in daily life?
Division is used for sharing equally, calculating per-unit costs (price per kg, per item), finding averages, converting units, and solving rate problems like speed, distance, and time.
Related Topics
- Division of Large Numbers
- Long Division
- Addition of Large Numbers
- Subtraction of Large Numbers
- Multiplication of Large Numbers
- Order of Operations (BODMAS)
- Word Problems on Four Operations
- Mental Math (Grade 5)
- Multiplication of 4-Digit Numbers
- Simplification Using BODMAS
- Properties of Operations (Grade 5)
- Unitary Method (Grade 5)
