Division of 2-Digit by 1-Digit
Division of a 2-digit number by a 1-digit number is the starting point of the long division method. Students learn to divide numbers from 10 to 99 by numbers from 1 to 9.
This skill builds directly on multiplication tables. If a student knows that 7 × 8 = 56, they can quickly find 56 ÷ 7 = 8.
What is Division of 2-Digit by 1-Digit - Class 4 Maths (Division (Grade 4))?
Dividing a 2-digit number by a 1-digit number means finding how many times the 1-digit number fits into the 2-digit number. The result is the quotient, and any leftover is the remainder.
Division is the reverse (or inverse) of multiplication.
Division of 2-Digit by 1-Digit Formula
Dividend ÷ Divisor = Quotient (Remainder)
Dividend = Divisor × Quotient + Remainder
Types and Properties
Two types of 2-digit ÷ 1-digit division:
- Exact division (remainder = 0): The divisor goes evenly into the dividend. Example: 48 ÷ 6 = 8.
- Division with remainder: There is a leftover. Example: 50 ÷ 7 = 7 remainder 1.
Solved Examples
Example 1: Example 1: Using Multiplication Tables
Problem: Divide 36 ÷ 4
Solution:
Think: 4 × ? = 36
4 × 9 = 36
Answer: 36 ÷ 4 = 9
Example 2: Example 2: Long Division Method
Problem: Divide 78 ÷ 3
Solution:
Step 1: 7 ÷ 3 = 2 (3 × 2 = 6). Subtract: 7 − 6 = 1.
Step 2: Bring down 8 → 18. 18 ÷ 3 = 6 (3 × 6 = 18). Subtract: 18 − 18 = 0.
Answer: 78 ÷ 3 = 26
Example 3: Example 3: Division with Remainder
Problem: Divide 47 ÷ 5
Solution:
Step 1: 4 ÷ 5 → 5 does not go into 4. Take 47.
47 ÷ 5 = 9 (5 × 9 = 45). Subtract: 47 − 45 = 2.
Answer: 47 ÷ 5 = 9 remainder 2
Check: 5 × 9 + 2 = 45 + 2 = 47 ✓
Example 4: Example 4: Equal Sharing Word Problem
Problem: Meera has 56 mangoes. She shares them equally among 8 friends. How many mangoes does each friend get?
Solution:
56 ÷ 8 = 7 (since 8 × 7 = 56)
Answer: Each friend gets 7 mangoes.
Example 5: Example 5: Grouping Word Problem
Problem: A florist has 65 flowers. She puts 7 flowers in each vase. How many vases does she fill? How many flowers are left?
Solution:
65 ÷ 7 = 9 remainder 2 (7 × 9 = 63; 65 − 63 = 2)
Answer: She fills 9 vases with 2 flowers left over.
Example 6: Example 6: When Tens Digit Is Divisible
Problem: Divide 93 ÷ 3
Solution:
Step 1: 9 ÷ 3 = 3. Write 3. Subtract: 9 − 9 = 0.
Step 2: Bring down 3. 3 ÷ 3 = 1. Write 1. Subtract: 3 − 3 = 0.
Answer: 93 ÷ 3 = 31
Example 7: Example 7: Division by 2 (Halving)
Problem: Divide 86 ÷ 2
Solution:
8 ÷ 2 = 4. Bring down 6. 6 ÷ 2 = 3.
Answer: 86 ÷ 2 = 43
This is the same as finding half of 86.
Example 8: Example 8: Money Word Problem
Problem: Aman has ₹95. He wants to buy pens costing ₹8 each. How many pens can he buy? How much money is left?
Solution:
95 ÷ 8 = 11 remainder 7 (8 × 11 = 88; 95 − 88 = 7)
Answer: Aman can buy 11 pens with ₹7 left over.
Example 9: Example 9: Verifying with Multiplication
Problem: Verify that 72 ÷ 9 = 8.
Solution:
Check: 9 × 8 = 72 ✓
Since divisor × quotient = dividend, the answer is correct.
Answer: Verified. 72 ÷ 9 = 8.
Example 10: Example 10: Finding Quotient and Remainder
Problem: Find the quotient and remainder when 59 is divided by 6.
Solution:
6 × 9 = 54 (closest to 59 without exceeding it)
Remainder = 59 − 54 = 5
Quotient = 9, Remainder = 5
Check: 6 × 9 + 5 = 54 + 5 = 59 ✓
Answer: Quotient = 9, Remainder = 5
Real-World Applications
Dividing 2-digit numbers by 1-digit numbers is used daily:
- Sharing: Dividing sweets, fruits, or items equally among friends.
- Money: Splitting a bill or dividing pocket money.
- Packing: Finding how many boxes are needed.
- Time: Converting 90 minutes into hours (90 ÷ 60 = 1 hour 30 minutes).
Key Points to Remember
- Division is the inverse of multiplication. Know your tables well.
- The remainder is always less than the divisor.
- If the tens digit is smaller than the divisor, divide the entire 2-digit number at once.
- Always check: Divisor × Quotient + Remainder = Dividend.
- Division by 1 gives the number itself: 57 ÷ 1 = 57.
- A number divided by itself gives 1: 57 ÷ 57 = 1.
Practice Problems
- Divide 84 ÷ 7.
- Find the quotient and remainder: 53 ÷ 6.
- Priya has 72 pencils. She distributes them equally among 9 students. How many pencils does each student get?
- Divide 99 ÷ 4. What is the remainder?
- Dev has ₹68. He buys samosas at ₹5 each. How many can he buy? How much money is left?
- Is 81 ÷ 9 exact (no remainder)? How do you know?
- Find 50 ÷ 3 and check your answer.
- A rope 76 cm long is cut into 8 equal pieces. How long is each piece? Is there any rope left?
Frequently Asked Questions
Q1. What if the tens digit is smaller than the divisor?
Divide the full 2-digit number by the divisor. For example, in 35 ÷ 6, since 3 < 6, consider 35 directly: 35 ÷ 6 = 5 remainder 5.
Q2. How are multiplication tables related to division?
Division is the reverse of multiplication. If 6 × 8 = 48, then 48 ÷ 6 = 8 and 48 ÷ 8 = 6. Knowing tables makes division faster.
Q3. Can the remainder be 0?
Yes. When the divisor divides the dividend exactly, the remainder is 0. For example, 42 ÷ 7 = 6 with remainder 0.
Q4. What is the largest possible remainder when dividing by 5?
The largest remainder is 4 (one less than the divisor). For example, 29 ÷ 5 = 5 remainder 4.
Q5. Can I divide by 0?
No. Division by 0 is undefined. You cannot share items into 0 groups — it has no meaning.
Q6. How do I check if my division answer is correct?
Multiply the quotient by the divisor and add the remainder. If you get back the dividend, the answer is correct. Example: 47 ÷ 5 = 9 R 2. Check: 5 × 9 + 2 = 47.
Q7. What is the quotient when a number is divided by 1?
The quotient equals the number itself. For example, 85 ÷ 1 = 85, because dividing into 1 group means the whole number stays.
Q8. Is 2-digit by 1-digit division in NCERT Class 4?
Yes. NCERT Class 4 Maths covers division of 2-digit and 3-digit numbers by 1-digit numbers using the long division method.
