Maths

Addition and Subtraction

Class 3

🎯 Learning Objectives

Add 3-digit and 4-digit numbers with carrying (regrouping).
Subtract 3-digit and 4-digit numbers with borrowing (regrouping).
Understand step-by-step working of carrying and borrowing.
Learn properties of addition (commutative, zero property).
Check subtraction answers using addition.
Solve word problems using addition and subtraction.

📖 Let Us Begin!

Meena's school collected 347 books in the first week and 285 books in the second week for a book donation drive. How many books were collected in all? To find out, we add the two numbers.

Sometimes when we add, the total in a column is more than 9. Then we carry the extra to the next column. This is called regrouping.

If the school gave away 268 books from a stock of 503, how many are left? We subtract. Sometimes the top digit is smaller, so we borrow from the next column.

Step-by-Step: Addition with Carrying

Example 1: 347 + 285

	H	T	O
	3	4	7
+	2	8	5
=	6	3	2

Step 1 (Ones): 7 + 5 = 12. Write 2 in the Ones column. Carry 1 to the Tens column.

Step 2 (Tens): 4 + 8 = 12, plus the carried 1 = 13. Write 3 in the Tens column. Carry 1 to the Hundreds column.

Step 3 (Hundreds): 3 + 2 = 5, plus the carried 1 = 6. Write 6 in the Hundreds column.

Answer: 347 + 285 = 632

Addition with Carrying: More Examples

Example 2: 456 + 378

Ones: 6 + 8 = 14, write 4, carry 1. Tens: 5 + 7 = 12, + 1 = 13, write 3, carry 1. Hundreds: 4 + 3 = 7, + 1 = 8.

Answer: 456 + 378 = 834

Example 3: 589 + 276

Ones: 9 + 6 = 15, write 5, carry 1. Tens: 8 + 7 = 15, + 1 = 16, write 6, carry 1. Hundreds: 5 + 2 = 7, + 1 = 8.

Answer: 589 + 276 = 865

Visual showing addition with carrying — groups of objects being combined with regrouping arrows

4-Digit Addition with Carrying

In Class 3, we also add 4-digit numbers. The method is the same — start from the Ones column and move left.

Example 4: 2,456 + 1,378

	Th	H	T	O
	2	4	5	6
+	1	3	7	8
=	3	8	3	4

Step 1 (Ones): 6 + 8 = 14. Write 4, carry 1.

Step 2 (Tens): 5 + 7 = 12, + 1 = 13. Write 3, carry 1.

Step 3 (Hundreds): 4 + 3 = 7, + 1 = 8. Write 8.

Step 4 (Thousands): 2 + 1 = 3. Write 3.

Answer: 2,456 + 1,378 = 3,834

Example 5: 4,567 + 3,895

Ones: 7 + 5 = 12, write 2, carry 1. Tens: 6 + 9 = 15, + 1 = 16, write 6, carry 1. Hundreds: 5 + 8 = 13, + 1 = 14, write 4, carry 1. Thousands: 4 + 3 = 7, + 1 = 8.

Answer: 4,567 + 3,895 = 8,462

Step-by-Step: Subtraction with Borrowing

Example 1: 503 − 268

	H	T	O
	5	0	3
−	2	6	8
=	2	3	5

Step 1 (Ones): 3 − 8? We cannot! Borrow 1 ten from the Tens column. But Tens column is 0, so borrow 1 hundred from the Hundreds column first. H becomes 4, T becomes 10. Now borrow 1 ten for Ones: T becomes 9, O becomes 13. Now 13 − 8 = 5.

Step 2 (Tens): 9 − 6 = 3.

Step 3 (Hundreds): 4 − 2 = 2.

Answer: 503 − 268 = 235

Subtraction with Borrowing: More Examples

Example 2: 700 − 356

Ones: 0 − 6? Cannot! Borrow from Tens. Tens is 0, so borrow from Hundreds first. H becomes 6, T becomes 10. Now borrow 1 for Ones: T becomes 9, O becomes 10. 10 − 6 = 4.

Tens: 9 − 5 = 4. Hundreds: 6 − 3 = 3.

Answer: 700 − 356 = 344

Example 3: 812 − 467

Ones: 2 − 7? Cannot! Borrow from Tens: T becomes 0, O becomes 12. 12 − 7 = 5.

Tens: 0 − 6? Cannot! Borrow from Hundreds: H becomes 7, T becomes 10. 10 − 6 = 4.

Hundreds: 7 − 4 = 3.

Answer: 812 − 467 = 345

Visual showing subtraction with borrowing on a number line

4-Digit Subtraction with Borrowing

Example 4: 5,003 − 2,768

	Th	H	T	O
	5	0	0	3
−	2	7	6	8
=	2	2	3	5

Step 1 (Ones): 3 − 8? Cannot! Tens is 0, Hundreds is 0. Borrow from Thousands: Th becomes 4, H becomes 10. Now borrow from H for T: H becomes 9, T becomes 10. Now borrow from T for O: T becomes 9, O becomes 13. 13 − 8 = 5.

Step 2 (Tens): 9 − 6 = 3.

Step 3 (Hundreds): 9 − 7 = 2.

Step 4 (Thousands): 4 − 2 = 2.

Answer: 5,003 − 2,768 = 2,235

Example 5: 7,200 − 3,856

Ones: 0 − 6? Cannot! Borrow step by step. T becomes 9, O becomes 10. 10 − 6 = 4.

Tens: 9 − 5 = 4. Hundreds: 1 − 8? Cannot! Borrow from Th: Th becomes 6, H becomes 11. 11 − 8 = 3. Thousands: 6 − 3 = 3.

Answer: 7,200 − 3,856 = 3,344

Checking Subtraction Using Addition

Think: If 503 − 268 = 235, then 235 + 268 should give us back 503. Let us check: 235 + 268 = 503. Correct!

Rule: Difference + Smaller Number = Bigger Number. If this is true, your subtraction is correct.

Check Example

812 − 467 = 345. Check: 345 + 467 = 812 ✓ Correct!

5,003 − 2,768 = 2,235. Check: 2,235 + 2,768 = 5,003 ✓ Correct!

Properties of Addition

Addition has some special rules that always work:

Property	What It Means	Example
Commutative Property (Order Property)	We can add two numbers in any order and the sum stays the same.	347 + 285 = 285 + 347 = 632
Zero Property (Identity Property)	Adding 0 to any number gives the same number.	456 + 0 = 456 0 + 789 = 789
Associative Property	When adding three numbers, we can group them in any way.	(2 + 3) + 4 = 2 + (3 + 4) = 9

Arjun says: "I can add 125 + 300 easily — it's 425. So 300 + 125 must also be 425!" He is using the commutative property.

Word Problems (Indian Context)

Problem 1: Money (₹ Rupees)

Ravi's father gave him ₹475 for books and ₹368 for a school bag. How much money did Ravi get in all?

Solution: ₹475 + ₹368 = ₹843. Ravi got ₹843 in all.

Problem 2: Cricket Scores

In a cricket match, India scored 256 runs in the first innings and 189 runs in the second innings. What was the total score?

Solution: 256 + 189 = 445 runs.

Problem 3: Train Passengers

A train had 1,250 passengers. At Delhi station, 486 passengers got down. How many passengers are still on the train?

Solution: 1,250 − 486 = 764 passengers are still on the train.

Problem 4: School Library

Meena's school library has 2,345 Hindi books and 1,678 English books. How many books are there in all?

Solution: 2,345 + 1,678 = 4,023 books in all.

Children at a book donation drive — word problem illustration

📝 Key Words

Word	Meaning
Carrying (Regrouping)	When the sum in a column is 10 or more, we write the ones digit and carry the tens digit to the next column
Borrowing (Regrouping)	When the top digit is smaller, we take 1 from the next column to make it bigger
Sum	The answer we get after adding
Difference	The answer we get after subtracting
Place Value	The value of a digit based on its position (Ones, Tens, Hundreds, Thousands)
Commutative Property	Numbers can be added in any order: a + b = b + a
Zero Property	Adding 0 to any number gives the same number

⭐ Key Points to Remember

Always start adding or subtracting from the Ones column (right side).
In addition, if a column total is 10 or more, carry to the next column.
In subtraction, if the top digit is smaller, borrow from the next column.
Check your subtraction: add the answer to the smaller number. You should get the bigger number.
Commutative property: a + b = b + a (order does not matter in addition).
Zero property: any number + 0 = the same number.
The same method works for 3-digit and 4-digit numbers.

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. 234 + 145 = ?

234 + 145 = 379.

2. 500 − 246 = ?

500 − 246 = 254.

3. The answer of an addition is called the:

The answer of an addition is the sum. The answer of a subtraction is the difference.

4. Which is the correct check for 367 + 218 = 585?

To check addition, subtract one number from the sum: 585 − 218 = 367.

5. 456 + 369 = ? (digits only)

456 + 369 = 825.

6. 623 − 435 = ? (digits only)

623 − 435 = 188.

7. Meena had 450 stickers and gave away 180. How many are left? (digits only)

450 − 180 = 270 stickers left.

8. A shop sold 320 mangoes on Monday and 380 on Tuesday. How many in all? (digits only)

320 + 380 = 700 mangoes.

✏️ Practice Questions

A. Fill in the Blanks (10 questions)

1. 347 + 285 =

2. 456 + 378 =

3. 700 − 356 =

4. 503 − 268 =

5. 2,456 + 1,378 =

6. 5,003 − 2,768 =

7. 389 + 0 = (Zero Property)

8. 275 + 486 = 486 + (Commutative Property)

9. 1,000 − 567 =

10. 3,456 + 2,789 =

B. Choose the Correct Answer (MCQ)

1. What is 589 + 276?

(a) 855(b) 865(c) 856(d) 875

2. What is 800 − 456?

(a) 354(b) 344(c) 444(d) 334

3. Which property says 25 + 0 = 25?

(a) Commutative(b) Zero Property(c) Associative(d) None

4. If 612 − 347 = 265, what is 265 + 347?

(a) 602(b) 612(c) 622(d) 512

5. What is 4,567 + 3,895?

(a) 8,462(b) 8,452(c) 8,362(d) 7,462

C. Word Problems

1. Arjun's father earned ₹4,500 in one week and ₹3,875 the next week. How much did he earn in total?

2. A cricket team scored 345 runs in the first match and 278 runs in the second match. What is the total score?

3. A train had 1,500 passengers. At Jaipur station, 687 passengers got down. How many passengers are still on the train?

4. Meena saved ₹2,350 in April and spent ₹1,475 on books in May. How much money does she have left?

5. A school has 1,236 boys and 1,189 girls. What is the total number of students? Check your answer.

D. True or False

1. 347 + 285 = 285 + 347.

2. In subtraction, we always start from the left (Thousands column).

3. Adding 0 to any number gives 0.

4. If 503 − 268 = 235, then 235 + 268 = 503.

5. Carrying means taking 1 from the next column.

E. Match the Following

Column A	Column B
1. 456 + 378	(a) 235
2. 503 − 268	(b) 344
3. 700 − 356	(c) 834
4. 389 + 0	(d) 3,834
5. 2,456 + 1,378	(e) 389

🎨 Think and Do — Fun Activity

Number Detective: Solve each subtraction below. Then check your answer by adding the difference to the smaller number. Write "Correct" or "Try Again" next to each.

1. 704 − 389 = _________ Check: _________ + 389 = _________

2. 561 − 275 = _________ Check: _________ + 275 = _________

3. 830 − 462 = _________ Check: _________ + 462 = _________

Challenge: Write your own 4-digit addition sum where carrying happens in all four columns. Solve it and ask a friend to check!

My sum: _________ + _________ = _________

Want to review the lesson again?

🎯 Learning Objectives

Add 3-digit and 4-digit numbers with carrying (regrouping).
Subtract 3-digit and 4-digit numbers with borrowing (regrouping).
Understand step-by-step working of carrying and borrowing.
Learn properties of addition (commutative, zero property).
Check subtraction answers using addition.
Solve word problems using addition and subtraction.

📖 Let Us Begin!

Meena's school collected 347 books in the first week and 285 books in the second week for a book donation drive. How many books were collected in all? To find out, we add the two numbers. Sometimes when we add, the total in a column is more than 9. Then we carry the extra to the next column. This is called regrouping.

If the school gave away 268 books from a stock of 503, how many are left? We subtract. Sometimes the top digit is smaller, so we borrow from the next column.

Step-by-Step: Addition with Carrying

Example 1: 347 + 285

	H	T	O
	3	4	7
+	2	8	5
=	6	3	2

Step 1 (Ones): 7+5=12. Write 2, carry 1. Step 2 (Tens): 4+8+1=13. Write 3, carry 1. Step 3 (Hundreds): 3+2+1=6. Answer: 632

More Addition Examples

Example 2: 456 + 378: O: 6+8=14 (write 4, carry 1). T: 5+7+1=13 (write 3, carry 1). H: 4+3+1=8. Answer: 834
Example 3: 589 + 276: O: 9+6=15 (write 5, carry 1). T: 8+7+1=16 (write 6, carry 1). H: 5+2+1=8. Answer: 865

4-Digit Addition with Carrying

Example 4: 2,456 + 1,378

	Th	H	T	O
	2	4	5	6
+	1	3	7	8
=	3	8	3	4

O: 6+8=14 (write 4, carry 1). T: 5+7+1=13 (write 3, carry 1). H: 4+3+1=8. Th: 2+1=3. Answer: 3,834

Example 5: 4,567 + 3,895: O: 7+5=12 (carry 1). T: 6+9+1=16 (carry 1). H: 5+8+1=14 (carry 1). Th: 4+3+1=8. Answer: 8,462

Step-by-Step: Subtraction with Borrowing

Example 1: 503 − 268

	H	T	O
	5	0	3
−	2	6	8
=	2	3	5

Step 1: 3−8? Cannot! T is 0, borrow from H. H→4, T→10. Borrow for O: T→9, O→13. 13−8=5. Step 2: 9−6=3. Step 3: 4−2=2. Answer: 235

More Subtraction Examples

Example 2: 700 − 356: Borrow step by step. O: 10−6=4. T: 9−5=4. H: 6−3=3. Answer: 344
Example 3: 812 − 467: O: 12−7=5. T: 0−6? Borrow. 10−6=4. H: 7−4=3. Answer: 345

4-Digit Subtraction with Borrowing

Example 4: 5,003 − 2,768

	Th	H	T	O
	5	0	0	3
−	2	7	6	8
=	2	2	3	5

Borrow chain: Th→4, H→10→9, T→10→9, O→13. O: 13−8=5. T: 9−6=3. H: 9−7=2. Th: 4−2=2. Answer: 2,235

Example 5: 7,200 − 3,856: Borrow step by step. O: 10−6=4. T: 9−5=4. H: 11−8=3. Th: 6−3=3. Answer: 3,344

Checking Subtraction Using Addition

If 503 − 268 = 235, then 235 + 268 should give us back 503. Check: 235 + 268 = 503. ✓ Correct!

Rule: Difference + Smaller Number = Bigger Number.

812 − 467 = 345. Check: 345 + 467 = 812 ✓
5,003 − 2,768 = 2,235. Check: 2,235 + 2,768 = 5,003 ✓

Properties of Addition

Property	Meaning	Example
Commutative (Order)	Add in any order, same answer	347 + 285 = 285 + 347 = 632
Zero (Identity)	Adding 0 gives the same number	456 + 0 = 456
Associative	Group in any way, same answer	(2+3)+4 = 2+(3+4) = 9

Arjun says: "125 + 300 = 425, so 300 + 125 = 425 too!" — Commutative property!

Word Problems (Indian Context)

1. Money: Ravi's father gave him ₹475 for books and ₹368 for a school bag. Total: 475 + 368 = ₹843
2. Cricket: India scored 256 runs (1st innings) + 189 runs (2nd innings) = 445 runs
3. Train: 1,250 passengers − 486 got down = 764 passengers still on train
4. Library: 2,345 Hindi books + 1,678 English books = 4,023 books in all

📝 Key Words

Word	Meaning
Carrying (Regrouping)	Sum in column ≥ 10: write ones digit, carry tens digit
Borrowing (Regrouping)	Top digit smaller: take 1 from next column
Sum	Answer after adding
Difference	Answer after subtracting
Place Value	Value based on position (O, T, H, Th)
Commutative Property	a + b = b + a
Zero Property	a + 0 = a

⭐ Key Points to Remember

Always start from the Ones column (right side).
In addition, if column total ≥ 10, carry to next column.
In subtraction, if top digit is smaller, borrow from next column.
Check subtraction: Difference + Smaller = Bigger number.
Commutative: a + b = b + a. Zero: a + 0 = a.
Same method works for 3-digit and 4-digit numbers.

A. Fill in the Blanks

1. 347 + 285 =

2. 456 + 378 =

3. 700 − 356 =

4. 503 − 268 =

5. 2,456 + 1,378 =

6. 5,003 − 2,768 =

7. 389 + 0 = (Zero Property)

8. 275 + 486 = 486 + (Commutative Property)

9. 1,000 − 567 =

10. 3,456 + 2,789 =

B. Choose the Correct Answer

1. What is 589 + 276?

(a) 855(b) 865(c) 856(d) 875

2. What is 800 − 456?

(a) 354(b) 344(c) 444(d) 334

3. Which property says 25 + 0 = 25?

(a) Commutative(b) Zero Property(c) Associative(d) None

4. If 612 − 347 = 265, what is 265 + 347?

(a) 602(b) 612(c) 622(d) 512

5. What is 4,567 + 3,895?

(a) 8,462(b) 8,452(c) 8,362(d) 7,462

C. Word Problems

1. Arjun's father earned ₹4,500 in one week and ₹3,875 the next week. How much did he earn in total?

2. A cricket team scored 345 runs in the first match and 278 runs in the second match. What is the total score?

3. A train had 1,500 passengers. At Jaipur station, 687 passengers got down. How many passengers are still on the train?

4. Meena saved ₹2,350 in April and spent ₹1,475 on books in May. How much money does she have left?

5. A school has 1,236 boys and 1,189 girls. What is the total number of students? Check your answer.

D. True or False

1. 347 + 285 = 285 + 347.

2. In subtraction, we always start from the left (Thousands column).

3. Adding 0 to any number gives 0.

4. If 503 − 268 = 235, then 235 + 268 = 503.

5. Carrying means taking 1 from the next column.

E. Match the Following

Column A	Column B
1. 456 + 378	(a) 235
2. 503 − 268	(b) 344
3. 700 − 356	(c) 834
4. 389 + 0	(d) 3,834
5. 2,456 + 1,378	(e) 389

🎨 Think and Do — Fun Activity

Number Detective: Solve each subtraction. Then check by adding the difference to the smaller number.

1. 704 − 389 = _________ Check: _________ + 389 = _________

2. 561 − 275 = _________ Check: _________ + 275 = _________

3. 830 − 462 = _________ Check: _________ + 462 = _________

Challenge: Write your own 4-digit addition sum where carrying happens in all four columns. Solve it!

My sum: _________ + _________ = _________

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Addition and Subtraction

🎯 Learning Objectives

📖 Let Us Begin!

Step-by-Step: Addition with Carrying

Addition with Carrying: More Examples

4-Digit Addition with Carrying

Step-by-Step: Subtraction with Borrowing

Subtraction with Borrowing: More Examples

4-Digit Subtraction with Borrowing

Checking Subtraction Using Addition

Properties of Addition

Word Problems (Indian Context)

📝 Key Words

🎯 Quick Quiz — Test Yourself!

✏️ Practice Questions

Addition and Subtraction

Addition and Subtraction (continued)

Addition and Subtraction (practice)