Maths

Division

Class 3

🎯 Learning Objectives

Understand division as equal sharing and grouping.
Learn division as repeated subtraction.
Know division facts from multiplication tables (2 to 10).
Perform long division of 2-digit numbers by 1-digit numbers.
Understand division with remainder.
Check division answers using the formula: Quotient × Divisor + Remainder = Dividend.

📖 What is Division?

Aarav has 12 laddoos. He wants to share them equally among 4 friends. How many laddoos will each friend get? To find out, we divide: 12 ÷ 4 = 3. Each friend gets 3 laddoos.

Division means splitting a number into equal parts. It is the opposite of multiplication. If 4 × 3 = 12, then 12 ÷ 4 = 3.

We can think of division in two ways:

Equal Sharing: Distributing items equally among a given number of groups. (How many in each group?)
Grouping: Making groups of a given size from a collection. (How many groups can we make?)

Division as Equal Sharing

When we share things equally, we use division.

Example 1: Sharing Laddoos

Priya made 20 laddoos for Diwali. She wants to pack them equally into 5 boxes. How many laddoos in each box?

Solution: 20 ÷ 5 = 4. Each box will have 4 laddoos.

Example 2: Distributing Notebooks

A teacher has 24 notebooks to distribute equally among 6 students. How many notebooks does each student get?

Solution: 24 ÷ 6 = 4. Each student gets 4 notebooks.

Division as Grouping

Sometimes we know the size of each group and want to find how many groups we can make.

Example 3: Making Teams

There are 18 children in a class. The teacher wants to make teams of 3. How many teams can be formed?

Solution: 18 ÷ 3 = 6. The teacher can make 6 teams.

Example 4: Packing Mangoes

A fruit seller has 30 mangoes. He puts 5 mangoes in each bag. How many bags does he need?

Solution: 30 ÷ 5 = 6. He needs 6 bags.

12 laddoos being shared equally into 4 plates showing division as sharing

Division as Repeated Subtraction

Division can also be understood as repeated subtraction. We keep subtracting the divisor from the dividend until we reach 0 (or a number smaller than the divisor). The number of times we subtract is the quotient.

Example: 15 ÷ 3 using Repeated Subtraction

15 − 3 = 12 (subtracted 1 time)

12 − 3 = 9 (subtracted 2 times)

9 − 3 = 6 (subtracted 3 times)

6 − 3 = 3 (subtracted 4 times)

3 − 3 = 0 (subtracted 5 times)

We subtracted 3 a total of 5 times. So, 15 ÷ 3 = 5.

Example: 20 ÷ 4 using Repeated Subtraction

20 − 4 = 16 → 16 − 4 = 12 → 12 − 4 = 8 → 8 − 4 = 4 → 4 − 4 = 0

We subtracted 4 a total of 5 times. So, 20 ÷ 4 = 5.

Division Facts from Multiplication Tables

Every multiplication fact gives us two division facts. If you know your tables, you can divide quickly!

Multiplication Fact	Division Fact 1	Division Fact 2
3 × 4 = 12	12 ÷ 3 = 4	12 ÷ 4 = 3
5 × 6 = 30	30 ÷ 5 = 6	30 ÷ 6 = 5
7 × 8 = 56	56 ÷ 7 = 8	56 ÷ 8 = 7
9 × 4 = 36	36 ÷ 9 = 4	36 ÷ 4 = 9
6 × 7 = 42	42 ÷ 6 = 7	42 ÷ 7 = 6
8 × 9 = 72	72 ÷ 8 = 9	72 ÷ 9 = 8

Think: If you know that 6 × 9 = 54, you instantly know that 54 ÷ 6 = 9 and 54 ÷ 9 = 6. Multiplication and division are like best friends!

Special Division Rules:

Any number ÷ 1 = the same number. (Example: 25 ÷ 1 = 25)
Any number ÷ itself = 1. (Example: 7 ÷ 7 = 1)
0 ÷ any number = 0. (Example: 0 ÷ 5 = 0)
We can never divide by 0. (Example: 8 ÷ 0 is not possible!)

Long Division (2-digit ÷ 1-digit)

For bigger numbers, we use long division. Let us learn the steps: Divide → Multiply → Subtract → Bring Down.

Example 1: 84 ÷ 4

Long Division
2 1 4 ) 8 4 −8 ↓ 0 4 −4 0

Step 1: Divide the tens digit. 8 ÷ 4 = 2. Write 2 in the quotient (tens place).

Step 2: Multiply. 2 × 4 = 8. Write 8 below 8.

Step 3: Subtract. 8 − 8 = 0.

Step 4: Bring down the ones digit (4). Now divide 4 ÷ 4 = 1. Write 1 in the quotient.

Step 5: Multiply. 1 × 4 = 4. Subtract. 4 − 4 = 0. Remainder = 0.

Answer: 84 ÷ 4 = 21

Long Division: Another Example

Example 2: 96 ÷ 3

Long Division
3 2 3 ) 9 6 −9 ↓ 0 6 −6 0

Step 1: Divide tens. 9 ÷ 3 = 3. Write 3 in quotient.

Step 2: Multiply. 3 × 3 = 9. Subtract. 9 − 9 = 0.

Step 3: Bring down 6. Divide 6 ÷ 3 = 2. Write 2 in quotient.

Step 4: Multiply. 2 × 3 = 6. Subtract. 6 − 6 = 0. Remainder = 0.

Answer: 96 ÷ 3 = 32

Example 3: 75 ÷ 5

Tens: 7 ÷ 5 = 1 (remainder 2). Multiply: 1 × 5 = 5. Subtract: 7 − 5 = 2. Bring down 5 → 25. Divide: 25 ÷ 5 = 5. Multiply: 5 × 5 = 25. Subtract: 25 − 25 = 0.

Answer: 75 ÷ 5 = 15

20 mangoes grouped into bags of 5 showing division as grouping

Division with Remainder

Sometimes a number does not divide exactly. The amount left over is called the remainder.

Example 1: 17 ÷ 5

How many times does 5 go into 17? → 5 × 3 = 15 (fits). 5 × 4 = 20 (too big!).

So, Quotient = 3. Remainder = 17 − 15 = 2.

Answer: 17 ÷ 5 = 3 remainder 2

We write: 17 = 5 × 3 + 2

Example 2: 23 ÷ 4

4 × 5 = 20 (fits). 4 × 6 = 24 (too big!).

Quotient = 5. Remainder = 23 − 20 = 3.

Answer: 23 ÷ 4 = 5 remainder 3

Example 3: 47 ÷ 6

6 × 7 = 42 (fits). 6 × 8 = 48 (too big!).

Quotient = 7. Remainder = 47 − 42 = 5.

Answer: 47 ÷ 6 = 7 remainder 5

Remember: The remainder is always less than the divisor. If the remainder is equal to or greater than the divisor, you need to divide one more time!

Checking Division

We can always check if our division answer is correct using this formula:

Quotient × Divisor + Remainder = Dividend

Check Example 1: 84 ÷ 4 = 21

Quotient = 21, Divisor = 4, Remainder = 0

Check: 21 × 4 + 0 = 84 ✓ Correct!

Check Example 2: 17 ÷ 5 = 3 remainder 2

Quotient = 3, Divisor = 5, Remainder = 2

Check: 3 × 5 + 2 = 15 + 2 = 17 ✓ Correct!

Check Example 3: 47 ÷ 6 = 7 remainder 5

Quotient = 7, Divisor = 6, Remainder = 5

Check: 7 × 6 + 5 = 42 + 5 = 47 ✓ Correct!

Word Problems (Indian Context)

Problem 1: Sharing Sweets

Meena's mother made 36 gulab jamuns for a party. She wants to serve them equally on 9 plates. How many gulab jamuns on each plate?

Solution: 36 ÷ 9 = 4. Each plate will have 4 gulab jamuns.

Problem 2: Distributing Books

The school library received 72 new books. The librarian wants to place them equally on 8 shelves. How many books on each shelf?

Solution: 72 ÷ 8 = 9. Each shelf will have 9 books.

Problem 3: Sharing Money (₹ Rupees)

Arjun's grandfather gave ₹45 to be shared equally among 5 grandchildren. How much does each grandchild get?

Solution: ₹45 ÷ 5 = ₹9. Each grandchild gets ₹9.

Problem 4: Packing Items

A shopkeeper has 50 pencils. He packs them in bundles of 6. How many full bundles can he make? How many pencils are left over?

Solution: 50 ÷ 6 = 8 remainder 2. He can make 8 full bundles with 2 pencils left over.

Problem 5: Arranging Chairs

For the school assembly, 63 chairs need to be arranged in 7 equal rows. How many chairs in each row?

Solution: 63 ÷ 7 = 9. Each row will have 9 chairs.

📝 Key Words

Word	Meaning
Division	Splitting a number into equal parts or groups
Dividend	The number being divided (the total)
Divisor	The number we divide by (number of groups or size of each group)
Quotient	The answer we get after dividing
Remainder	The amount left over when division is not exact
Equal Sharing	Distributing items equally among groups
Grouping	Making groups of a fixed size from a collection
Repeated Subtraction	Subtracting the divisor again and again until we reach 0 or less than the divisor
Long Division	A step-by-step method to divide larger numbers (Divide → Multiply → Subtract → Bring Down)
Inverse Operation	Division is the inverse (opposite) of multiplication

⭐ Key Points to Remember

Division means sharing equally or making equal groups.
Division is the opposite of multiplication. If a × b = c, then c ÷ a = b and c ÷ b = a.
In long division, follow: Divide → Multiply → Subtract → Bring Down.
The remainder is always less than the divisor.
To check: Quotient × Divisor + Remainder = Dividend.
Any number ÷ 1 = the same number. Any number ÷ itself = 1.
0 ÷ any number = 0. We can never divide by 0.

Finished learning? Now test what you know!

🎯 Quick Quiz — Test Yourself!

Answer these questions right here. You get instant feedback — no paper needed!

Score: 0 / 8

1. 42 ÷ 6 = ?

42 ÷ 6 = 7 (because 6 × 7 = 42).

2. The answer of a division is called the:

The answer of a division is called the quotient.

3. Any number divided by 1 gives:

Dividing by 1 does not change the number: 9 ÷ 1 = 9.

4. In 20 ÷ 3, the remainder is:

3 × 6 = 18, and 20 − 18 = 2. So quotient 6, remainder 2.

5. 56 ÷ 7 = ?

56 ÷ 7 = 8.

6. 81 ÷ 9 = ?

81 ÷ 9 = 9.

7. 24 laddoos are shared equally among 4 children. How many does each get?

24 ÷ 4 = 6 laddoos each.

8. 50 ÷ 5 = ?

50 ÷ 5 = 10.

✏️ Practice Questions

A. Fill in the Blanks (10 questions)

1. 24 ÷ 6 =

2. 45 ÷ 9 =

3. 56 ÷ 7 =

4. 72 ÷ 8 =

5. 84 ÷ 4 =

6. 96 ÷ 3 =

7. 35 ÷ 5 =

8. 63 ÷ 9 =

9. 48 ÷ 6 =

10. 81 ÷ 9 =

B. Choose the Correct Answer (MCQ — 5 questions)

1. What is 42 ÷ 7?

(a) 5(b) 6(c) 7(d) 8

2. What is the remainder when 29 ÷ 4?

(a) 0(b) 1(c) 2(d) 3

3. In 36 ÷ 6 = 6, what is the dividend?

(a) 6(b) 36(c) 0(d) 12

4. Which of these has a remainder of 0?

(a) 17 ÷ 3(b) 25 ÷ 4(c) 32 ÷ 8(d) 19 ÷ 5

5. 0 ÷ 8 = ?

(a) 8(b) 1(c) 0(d) Cannot divide

C. Word Problems (5 questions)

1. Sita has 28 laddoos. She shares them equally among 7 friends. How many laddoos does each friend get?

2. A teacher distributes 54 notebooks equally among 6 students. How many notebooks does each student get?

3. Ravi has ₹60. He wants to buy pens that cost ₹8 each. How many pens can he buy? How much money is left?

4. 45 students are going on a trip. Each auto-rickshaw can carry 4 students. How many auto-rickshaws are needed?

5. Priya's mother packed 48 rotis equally into 6 tiffin boxes. How many rotis are in each box?

D. Find the Quotient and Remainder (5 questions)

1. 25 ÷ 4 = Quotient: Remainder:

2. 38 ÷ 5 = Quotient: Remainder:

3. 53 ÷ 7 = Quotient: Remainder:

4. 67 ÷ 9 = Quotient: Remainder:

5. 79 ÷ 8 = Quotient: Remainder:

E. Check the Division (5 questions)

1. 30 ÷ 7 = 4 remainder 2. Check: 4 × 7 + 2 = . Is it correct?

2. 50 ÷ 6 = 8 remainder 2. Check: 8 × 6 + 2 = . Is it correct?

3. 43 ÷ 5 = 8 remainder 3. Check: 8 × 5 + 3 = . Is it correct?

4. 65 ÷ 8 = 8 remainder 1. Check: 8 × 8 + 1 = . Is it correct?

5. 77 ÷ 9 = 8 remainder 5. Check: 8 × 9 + 5 = . Is it correct?

🎨 Think and Do — Fun Activity

Division Sharing Game: Take 20 small objects (seeds, buttons, or coins). Try sharing them equally among different numbers of friends:

1. Share 20 objects among 4 friends. Each gets _________ objects. Left over: _________

2. Share 20 objects among 3 friends. Each gets _________ objects. Left over: _________

3. Share 20 objects among 6 friends. Each gets _________ objects. Left over: _________

4. Share 20 objects among 7 friends. Each gets _________ objects. Left over: _________

Challenge: Can you find a number between 1 and 10 that divides 20 exactly (remainder = 0)? Write all such numbers: _________________________

Want to review the lesson again?

🎯 Learning Objectives

Understand division as equal sharing and grouping.
Learn division as repeated subtraction.
Know division facts from multiplication tables (2 to 10).
Perform long division of 2-digit numbers by 1-digit numbers.
Understand division with remainder.
Check division answers using: Quotient × Divisor + Remainder = Dividend.

📖 What is Division?

Aarav has 12 laddoos. He wants to share them equally among 4 friends. How many laddoos will each friend get? We divide: 12 ÷ 4 = 3. Each friend gets 3 laddoos.

Division means splitting a number into equal parts. It is the opposite of multiplication. If 4 × 3 = 12, then 12 ÷ 4 = 3.

Two ways to think about division:

Equal Sharing: Distributing items equally among groups.
Grouping: Making groups of a given size from a collection.

Division as Equal Sharing

Example 1: Priya made 20 laddoos. She packs them equally into 5 boxes. 20 ÷ 5 = 4 laddoos per box.
Example 2: A teacher has 24 notebooks for 6 students. 24 ÷ 6 = 4 notebooks each.

Division as Grouping

Example 3: 18 children, teams of 3. 18 ÷ 3 = 6 teams.
Example 4: 30 mangoes, 5 per bag. 30 ÷ 5 = 6 bags.

Division as Repeated Subtraction

15 ÷ 3: 15−3=12, 12−3=9, 9−3=6, 6−3=3, 3−3=0. Subtracted 5 times. Answer: 5
20 ÷ 4: 20−4=16, 16−4=12, 12−4=8, 8−4=4, 4−4=0. Subtracted 5 times. Answer: 5

Division Facts from Multiplication Tables

Multiplication Fact	Division Fact 1	Division Fact 2
3 × 4 = 12	12 ÷ 3 = 4	12 ÷ 4 = 3
5 × 6 = 30	30 ÷ 5 = 6	30 ÷ 6 = 5
7 × 8 = 56	56 ÷ 7 = 8	56 ÷ 8 = 7
9 × 4 = 36	36 ÷ 9 = 4	36 ÷ 4 = 9
6 × 7 = 42	42 ÷ 6 = 7	42 ÷ 7 = 6
8 × 9 = 72	72 ÷ 8 = 9	72 ÷ 9 = 8

Special Rules: a ÷ 1 = a | a ÷ a = 1 | 0 ÷ a = 0 | Cannot divide by 0

Long Division (2-digit ÷ 1-digit)

Steps: Divide → Multiply → Subtract → Bring Down

Example 1: 84 ÷ 4 = 21
Step 1: 8 ÷ 4 = 2 (write in quotient). Multiply: 2×4=8. Subtract: 8−8=0.
Step 2: Bring down 4. 4 ÷ 4 = 1. Multiply: 1×4=4. Subtract: 4−4=0. Remainder = 0.

Example 2: 96 ÷ 3 = 32
Step 1: 9 ÷ 3 = 3. Multiply: 3×3=9. Subtract: 9−9=0.
Step 2: Bring down 6. 6 ÷ 3 = 2. Multiply: 2×3=6. Subtract: 6−6=0. Remainder = 0.

Example 3: 75 ÷ 5 = 15
7 ÷ 5 = 1 (rem 2). Bring down 5 → 25. 25 ÷ 5 = 5. Answer: 15

Division with Remainder

Sometimes a number does not divide exactly. The amount left over is the remainder.

17 ÷ 5: 5×3=15 (fits). 17−15=2. Quotient = 3, Remainder = 2
23 ÷ 4: 4×5=20 (fits). 23−20=3. Quotient = 5, Remainder = 3
47 ÷ 6: 6×7=42 (fits). 47−42=5. Quotient = 7, Remainder = 5

Remember: The remainder is always less than the divisor!

Checking Division

Quotient × Divisor + Remainder = Dividend

Check 84 ÷ 4 = 21: 21 × 4 + 0 = 84 ✓
Check 17 ÷ 5 = 3 rem 2: 3 × 5 + 2 = 15 + 2 = 17 ✓
Check 47 ÷ 6 = 7 rem 5: 7 × 6 + 5 = 42 + 5 = 47 ✓

Word Problems (Indian Context)

1. Sharing Sweets: Meena's mother made 36 gulab jamuns for 9 plates. 36 ÷ 9 = 4 per plate.
2. Distributing Books: 72 books on 8 shelves. 72 ÷ 8 = 9 books per shelf.
3. Sharing Money: ₹45 among 5 grandchildren. 45 ÷ 5 = ₹9 each.
4. Packing Items: 50 pencils in bundles of 6. 50 ÷ 6 = 8 bundles, 2 left over.
5. Arranging Chairs: 63 chairs in 7 rows. 63 ÷ 7 = 9 chairs per row.

📝 Key Words

Word	Meaning
Division	Splitting a number into equal parts or groups
Dividend	The number being divided (the total)
Divisor	The number we divide by
Quotient	The answer after dividing
Remainder	Amount left over when division is not exact
Equal Sharing	Distributing items equally among groups
Grouping	Making groups of a fixed size
Repeated Subtraction	Subtracting divisor again and again until 0
Long Division	Step-by-step method: Divide → Multiply → Subtract → Bring Down
Inverse Operation	Division is the opposite of multiplication

⭐ Key Points to Remember

Division means sharing equally or making equal groups.
Division is the opposite of multiplication.
Long division steps: Divide → Multiply → Subtract → Bring Down.
Remainder is always less than the divisor.
Check: Quotient × Divisor + Remainder = Dividend.
a ÷ 1 = a. a ÷ a = 1. 0 ÷ a = 0. Cannot divide by 0.

A. Fill in the Blanks

1. 24 ÷ 6 =

2. 45 ÷ 9 =

3. 56 ÷ 7 =

4. 72 ÷ 8 =

5. 84 ÷ 4 =

6. 96 ÷ 3 =

7. 35 ÷ 5 =

8. 63 ÷ 9 =

9. 48 ÷ 6 =

10. 81 ÷ 9 =

B. Choose the Correct Answer

1. What is 42 ÷ 7?

(a) 5(b) 6(c) 7(d) 8

2. What is the remainder when 29 ÷ 4?

(a) 0(b) 1(c) 2(d) 3

3. In 36 ÷ 6 = 6, what is the dividend?

(a) 6(b) 36(c) 0(d) 12

4. Which has remainder 0?

(a) 17÷3(b) 25÷4(c) 32÷8(d) 19÷5

5. 0 ÷ 8 = ?

(a) 8(b) 1(c) 0(d) Cannot divide

C. Word Problems

1. Sita has 28 laddoos. She shares them equally among 7 friends. How many laddoos does each friend get?

2. A teacher distributes 54 notebooks equally among 6 students. How many notebooks does each student get?

3. Ravi has ₹60. He wants to buy pens that cost ₹8 each. How many pens can he buy? How much money is left?

4. 45 students are going on a trip. Each auto-rickshaw can carry 4 students. How many auto-rickshaws are needed?

5. Priya's mother packed 48 rotis equally into 6 tiffin boxes. How many rotis are in each box?

D. Find the Quotient and Remainder

1. 25 ÷ 4 = Q: R:

2. 38 ÷ 5 = Q: R:

3. 53 ÷ 7 = Q: R:

4. 67 ÷ 9 = Q: R:

5. 79 ÷ 8 = Q: R:

E. Check the Division

1. 30 ÷ 7 = 4 rem 2. Check: 4×7+2 = . Correct?

2. 50 ÷ 6 = 8 rem 2. Check: 8×6+2 = . Correct?

3. 43 ÷ 5 = 8 rem 3. Check: 8×5+3 = . Correct?

4. 65 ÷ 8 = 8 rem 1. Check: 8×8+1 = . Correct?

5. 77 ÷ 9 = 8 rem 5. Check: 8×9+5 = . Correct?

🎨 Think and Do — Fun Activity

Division Sharing Game: Take 20 small objects. Share them equally:

1. Among 4 friends: Each gets _________ Left over: _________

2. Among 3 friends: Each gets _________ Left over: _________

3. Among 6 friends: Each gets _________ Left over: _________

4. Among 7 friends: Each gets _________ Left over: _________

Challenge: Which numbers (1–10) divide 20 exactly? _________________________

You are viewing the worksheet layout. Click Print to save as PDF or print on A4 paper.

Division

🎯 Learning Objectives

📖 What is Division?

Division as Equal Sharing

Division as Grouping

Division as Repeated Subtraction

Division Facts from Multiplication Tables

Long Division (2-digit ÷ 1-digit)

Long Division: Another Example

Division with Remainder

Checking Division

Word Problems (Indian Context)

📝 Key Words

🎯 Quick Quiz — Test Yourself!

✏️ Practice Questions

Division

Division (continued)

Division (practice)