Addition of 4-Digit Numbers

We will learn about the addition of 4-digit numbers (without carrying and with carrying).

We know how to add 2 or 3, 3-digit numbers without carrying or with carrying. Now we will apply the same method when we add two 4-digit numbers (without carrying and with carrying) and three 4-digit numbers (without carrying and with carrying). The numbers which are added are called addends and the result obtained is called sum. The rules for addition of 4-digit numbers with other numbers are the same as that for the numbers having less digits.

I. Addition of 4-Digit Numbers Without Carrying:

(i) Add 2431 and 5327

$Addition of 4-Digit Numbers Without Carrying$

Step 1: Arrange the number in columns of thousands, hundreds tens and ones.

Step 2: Add ones.

Step 3: Then add tens.

Step 4: Then add hundreds.

Step 5: At last, add thousands.

(ii) Add 6132 and 3425.

Adding ones

Th H T O

6 1 3 2

+ 3 4 2 5

Adding tens

Th H T O

6 1 3 2

+ 3 4 2 5

5 7

Adding hundreds

Th H T O

6 1 3 2

+ 3 4 2 5

5 5 7

Adding thousands

Th H T O

6 1 3 2

+ 3 4 2 5

9 5 5 7

When we add 4-digit numbers, we first add the ones, then the tens, then the hundreds and lastly the thousands.

(iii) Add 3143 and 4522

$Addition of 4-Digit Numbers$

II. Addition of 4-Digit Numbers With Carrying:

Regrouping Ones -

(i) Add 5347 and 3237

Th H T O

5 3 4 7

+ 3 2 3 7

Adding ones:

7 + 7 = 14

14 = 1 ten + 4 ones

write 4 under O, carry 1 ten to T.

Th H T O

5 3 4 7

+ 3 2 3 7

8 4

Adding tens:

1 + 4 + 3 = 8 Write 8 under T

Th H T O

5 3 4 7

+ 3 2 3 7

5 8 4

Adding hundreds:

3 + 2 = 5 Write 5 under H

Th H T O

5 3 4 7

+ 3 2 3 7

8 5 8 4

Adding thousands:

5 + 3 = 8 Write 8 under Th

Regrouping Ones and Tens -

(ii) Add 4678 and 3239

Th H T O

4 6 7 8

+ 3 2 3 9

Adding Ones:

8 + 9 = 17

17 = 1 ten + 7 ones

write 7 under O, carry 1 ten to T.

Th H T O

1 1

4 6 7 8

+ 3 2 3 9

1 7

Adding Tens:

1 + 7 + 3 = 11

or 10 tens + 1 tens

or 1 hundred + 1 tens

Write 1 under T, carry 1 hundred to H

Th H T O

1 1

4 6 7 8

+ 3 2 3 9

9 1 7

Adding Hundreds:

1 + 6 + 2 = 9

Write 9 under H

Th H T O

1 1

4 6 7 8

+ 3 2 3 9

7 9 1 7

Adding Thousands:

4 + 3 = 7

Write 7 under Th

Regrouping Ones, Tens and Hundreds -

(iii) Add 4967 and 1757

Th H T O

4 9 6 7

+ 1 7 5 7

Adding Ones:

7 + 7 = 14

14 = 1 ten + 4 ones

write 4 under O, carry 1 ten to T.

Th H T O

1 1

4 9 6 7

+ 1 7 5 7

2 4

Adding Tens:

1 + 6 + 5 = 12

or 10 tens + 2 tens

or 1 hundred + 2 tens

Write 2 under T, carry 1 hundred to H.

Th H T O

1 1 1

4 9 6 7

+ 1 7 5 7

7 2 4

Adding Hundreds:

1 + 9 + 7 = 17

or 10 hundreds + 7 hundreds

or 1 thousand + 7 hundreds

Write 7 under H, carry 1 thousand to Th.

Th H T O

1 1 1

4 9 6 7

+ 1 7 5 7

6 7 2 4

Adding Thousands:

1 + 4 + 1= 6

Write 6 under Th.

(iv) Add 6376 and 2854

Adding ones

6 3 7 6

+ 2 8 5 4

Add ones i.e., 6 + 4 = 10. Write 0 below in ones column and carrying 1 into the tens column.

Adding tens

1 1

6 3 7 6

+ 2 8 5 4

3 0

Add tens i.e., 1 + 7 + 5 = 13. Write 3 below in tens column and carrying 1 into the hundreds column.

Adding hundreds

1 1

6 3 7 6

+ 2 8 5 4

2 3 0

Add hundreds i.e., 1 + 3 + 8 = 12. Write 2 below in hundreds column and carrying 1 into the thousands column.

Adding thousands

6 3 7 6

+ 2 8 5 4

9 2 3 0

Add thousands i.e., 1 + 6 + 2 = 9. Write 9 below in thousands column.

Adding 4-Digit Numbers with Regrouping:

(v) Add two 4-digit numbers 4187 and 3966 with regrouping.

Solution:

Step 1: Add the ones:

7 + 6 = 13 ones

13 ones = 1 ten + 3 ones

Write 3 in the ones place and carry 1 to the tens place.

$Add the Ones$

Step 2: Add the tens:

1 + 8 + 6 = 15

15 tens = 10 tens + 5 tens

= 1 hundred + 5 tens

Write 5 in the tens place and carry 1 to the hundreds place.

$Add the Tens$

Step 3: Add the hundreds:

1 + 1 + 9 = 11

11 hundreds = 10 hundreds +1 hundred

= 1 thousand + 1 hundred

Write 1 in the hundreds place and carry 1 to the thousands place.

$Add the Hundreds$

Step 4: Add the thousands:

1 + 4 + 3 = 8 thousands

Write 8 in the thousands place.

$Add the Thousands$

Answer: 4187 + 3966 = 8153

III. Similarly add three 4-digit numbers using the above rules for without and with carrying.

Addition of three 4-digit numbers without Regrouping:

(i) Find the sum of 5021, 3203 and 1210.

Th H T O

5 0 2 1

3 2 0 3

+ 1 2 1 0

9 4 3 4

Arrange the numbers in columns and add column wise.

Addition of three 4-digit numbers with Regrouping:

(ii) Find the sum of 2543, 1893 and 2678.

2 2 1

Th H T O

2 5 4 3

1 8 9 3

+ 2 6 7 8

7 1 1 4

Arrange the numbers in columns and add column wise.

(iii) Add 1223; 2346 and 3628.

Solution:

Addition of more than two numbers is similar as 2 numbers addition.

Step 1: Add ones.

Step 2: Add tens.

Step 3: Add hundreds.

Step 4: Add thousands.

$Addition of Three 4-Digit Numbers$

Answer: 1223 + 2346 + 3628 = 7197

Properties of Addition of 4-Digit Numbers:

Property I: When we change the order of 4-digit numbers while adding, the sum does not change.

1723 + 1804 = 3527

1804 + 1723 = 3527

Property II: When we add 0 to a 4-digit number or a number to 0, the sum is the number itself.

1532 + 0 = 1532

0 + 8545 = 8545

Property III: When we add 1 to a 4-digit number, the sum is the successor of that number.

2456 + 1 = 2457

7599 + 1 = 7600

Questions and Answers on Addition of 4-Digit Numbers:

I. Solved the sums: Addition of 4-digit without Regrouping

(i)	2 3 9 2 + 5 1 0 6 _________	(ii)	4 5 6 7 + 2 3 3 1 __________
(iii)	5 8 2 9 + 2 1 7 0 _________	(iv)	2 3 1 4 + 3 3 7 5
(v)	2 1 5 7 + 3 4 2 1 _________	(vi)	1 4 5 6 + 8 2 3 2
(vii)	3 2 0 3 + 3 7 2 5 _________	(viii)	2 3 1 4 + 2 1 1 + 3 2 3 3 __________
(ix)	4 5 6 3 + 1 3 + 3 4 2 2 _________	(x)	3 4 2 3 + 2 3 2 0 + 2 4 5 __________
(xi)	8 1 2 3 + 5 2 2 + 1 1 2 3 ________	(xii)	2 3 3 3 + 3 3 0 4 + 4 3 5 1 _________
(xiii)	2 1 5 6 + 6 3 2 + 4 1 0 1 _________	(xiv)	4 1 8 6 + 1 4 0 1 + 3 1 2 __________
(xv)	7 5 4 6 + 1 1 2 0 + 1 2 1 2 _________	(xvi)	6 8 3 2 + 1 0 1 4 + 2 1 3 2 _________
(xvii)	5 4 3 2 + 1 2 2 3 + 2 1 2 4 _______	(xviii)	4 1 2 3 + 2 3 2 5 + 2 3 2 1 ________
(xix)	5 2 1 2 + 1 5 2 4 + 1 1 3 2 + 2 1 2 1 ________	(xx)	2 1 2 1 + 1 2 1 2 + 2 1 2 1 + 1 2 1 2 ________
(xxi)	3 3 3 3 + 2 2 2 2 + 1 1 1 1 + 1 0 2 3 _________	(xxii)	7 2 2 1 + 4 4 2 + 3 4 + 2 __________
(xxiii)	5 3 4 3 + 2 1 0 2 + 5 2 3 + 3 1 _________	(xxiv)	3 4 2 1 + 1 1 2 2 + 3 2 2 3 + 2 2 2 3 ________
(xxv)	4 2 2 3 + 3 2 3 1 + 1 2 1 3 + 1 2 1 2 _________

Answer:

I. (i) 7498

(ii) 6898

(iii) 7999

(iv) 5689

(v) 5578

(vi) 9688

(vii) 6928

(viii) 5758

(ix) 7998

(x) 5988

(xi) 9768

(xii) 9988

(xiii) 6889

(xiv) 5899

(xv) 9878

(xvi) 9978

(xvii) 8779

(xviii) 8769

(xix) 9989

(xx) 6666

(xxi) 7689

(xxii) 7699

(xxiii) 7999

(xxiv) 9989

(xxv) 9879

II. Find the Addition of 4-Digit numbers Without Regrouping:

(i) 4251 + 1231

(ii) 1174 + 2012 + 3413

(iii) 4123 + 1532 + 4332

(iv) 1221 + 2112 + 3221 + 1020

(v) 1000 + 1222 + 3333 + 40

(vi) 3254 + 302 + 3241

(vii) 234 + 413 + 3132

(viii) 3132 + 154 + 4712

(ix) 3246 + 123 + 22 + 240

(x) 2611 + 1240 + 1023 + 22

(xi) 2301 + 2050 + 1432 + 800

(xii) 2115 + 1132 + 4130 + 1620

(xiii) 2113 + 520 + 1233 + 120

(xiv) 2323 + 1204 + 411 + 5000

(xv) 1134 + 320 + 33 + 7412

(xvi) 6321 + 1341 + 202 + 1122

Answer:

II. (i) 5482

(ii) 6599

(iii) 9987

(iv) 7574

(v) 5595

(vi) 6797

(vii) 3779

(viii) 7998

(ix) 3631

(x) 4896

(xi) 6583

(xii) 8997

(xiii) 3986

(xiv) 8938

(xv) 8899

(xvi) 8986

III. Add the following: Addition of 4-digit Numbers with Regrouping Ones -

(i)

Th H T O

4 3 2 7

+ 2 3 3 4

_________________

(ii)

Th H T O

3 2 1 9

+ 4 4 3 3

_________________

(iii)

Th H T O

5 6 7 8

+ 2 2 1 8

_________________

(iv)

Th H T O

8 8 4 2

+ 1 1 4 9

_________________

(v)

Th H T O

4 3 2 7

+ 2 2 2 2

+ 2 3 3 4

_________________

(vi)

Th H T O

3 2 1 9

+ 3 2 3 2

+ 3 2 4 2

_________________

(vii)

Th H T O

2 3 5 8

+ 1 6 2 8

+ 4 0 1 2

_________________

(viii)

Th H T O

6 2 0 1

+ 2 3 7 6

+ 1 0 1 9

_________________

(ix)

Th H T O

1 3 2 1

+ 1 3 0 5

+ 1 1 2 6

+ 1 1 1 3

_________________

(x)

Th H T O

2 4 1 2

+ 1 1 1 1

+ 3 2 3 3

+ 3 2 2 8

_________________

(xi)

Th H T O

1 2 3 4

+ 4 3 2 1

+ 1 0 0 3

+ 1 2 3 4

_________________

(xii)

Th H T O

5 2 1 1

+ 1 0 2 6

+ 2 4 3 4

+ 1 2 2 5

_________________

(xiii)

Th H T O

3 4 2 7

+ 1 1 3 5

+ 2 2 0 4

+ 3 1 3 3

_________________

(xiv)

Th H T O

2 3 3 2

+ 2 0 1 6

+ 2 3 2 8

+ 2 2 1 3

_________________

Answer:

III. (i) 6661

(ii) 7652

(iii) 7896

(iv) 9991

(v) 8883

(vi) 9693

(vii) 7998

(viii) 9596

(ix) 4865

(x) 9984

(xi) 7792

(xii) 9896

(xiii) 9899

(xiv) 8889

IV: Find the Addition of 4-Digit Numbers with Regrouping Ones - in your Notebook:

(i) 2231 + 4239 + 3 + 20

(ii) 4208 + 3012 + 2011 + 0010

(iii) 5217 + 14 + 62 + 102

(iv) 6224 + 45 + 6 + 1120

(v) 8337 + 1234 + 2 + 0

(vi) 3109 + 45 + 1132 + 0004

(vii) 2153 + 4218 + 1 + 320

(viii) 1234 + 26 +3213 + 3211

Answer:

IV. (i) 6493

(ii) 9241

(iii) 5395

(iv) 7395

(v) 9573

(vi) 4290

(vii) 6692

(viii) 7684

V. Add the following: Addition of 4-Digit Numbers with Regrouping Ones and Tens -

(i)

Th H T O

1 2 4 5

+ 3 2 6 6

_________________

(ii)

Th H T O

2 1 3 6

+ 3 5 7 7

_________________

(iii)

Th H T O

1 2 2 9

+ 5 2 8 6

_________________

(iv)

Th H T O

5 6 7 1

+ 4 2 8 9

_________________

(v)

Th H T O

4 3 5 5

+ 1 2 6 4

+ 2 1 8 5

_________________

(vi)

Th H T O

3 3 1 7

+ 1 2 8 4

+ 3 2 5 2

_________________

(vii)

Th H T O

1 3 2 6

+ 2 0 5 9

+ 1 5 3 3

_________________

(viii)

Th H T O

5 3 2 8

+ 1 4 3 1

+ 2 1 9 5

_________________

(ix)

Th H T O

1 4 5 3

+ 2 3 4

+ 4 2

+ 3

_________________

(x)

Th H T O

2 3 3 6

+ 1 6 3

+ 5 5

+ 2

_________________

(xi)

Th H T O

6 2 4 9

+ 1 5 0

+ 4 2

+ 3

_________________

(xii)

Th H T O

8 3 1 5

+ 2 3 6

+ 9 2

+ 3

_________________

(xiii)

Th H T O

2 4 6 7

+ 2 3 4 5

+ 1 0 2

+ 5 4

_________________

(xiv)

Th H T O

5 2 5 6

+ 2 4 3 4

+ 2 2 3

+ 6 4

_________________

(xv)

Th H T O

3 4 7 3

+ 3 2 2 4

+ 2 4 5

+ 3 6

_________________

(xvi)

Th H T O

7 1 2 7

+ 2 4 3 2

+ 2 3 4

+ 6 6

_________________

(xvii)

Th H T O

2 3 5 1

+ 1 0 6 5

+ 2 2 3 2

+ 2 4 8

_________________

(xviii)

Th H T O

5 1 3 7

+ 2 5 6

+ 2 3 5 1

+ 1 2 2 3

_________________

(xix)

Th H T O

4 1 5 6

+ 1 3 2 6

+ 1 4 0

+ 2 2 7 2

_________________

(xx)

Th H T O

3 5 6 2

+ 2 1 6 6

+ 0 3 3

+ 4 2 2 5

_________________

Answer:

VI: Do these 4-Digit Addition Numbers with Regrouping Ones and Tens - Sums in your Notebook:

(i) 3472 + 2468

(ii) 1468 + 3458

(iii) 3457 + 2358

(iv) 3437 + 2186

(v) 5086 + 1234 + 1270

(vi) 1635 + 3040 + 2256

(vii) 4238 + 2438 + 1253

(viii) 5188 + 2104 + 1386

(ix) 1245 + 5245 + 2243 + 1245

(x) 2128 + 2042 + 2341 + 2468

(xi) 5245 + 1356 + 2063 + 1025

(xii) 1274 + 2239 + 1143 + 1243

Answer:

VI:

VII. Add the following: Addition of 4-Digit Numbers with Regrouping Ones, Tens and Hundreds -

(i)

Th H T O

5 7 6 4

+ 2 6 4 9

_________________

(ii)

Th H T O

7 8 3 6

+ 1 4 9 9

_________________

(iii)

Th H T O

6 3 8 9

+ 2 8 7 7

_________________

(iv)

Th H T O

4 5 3 6

+ 2 6 8 7

_________________

(v)

Th H T O

4 6 7 8

+ 3 9 8 9

_________________

(vi)

Th H T O

2 4 6 8

+ 2 5 8 9

_________________

(vii)

Th H T O

3 2 8 2

+ 2 8 8 8

_________________

(viii)

Th H T O

4 3 7 8

+ 3 7 6 4

_________________

(ix)

Th H T O

5 8 6 7

+ 3 6 5 4

_________________

(x)

Th H T O

6 2 9 7

+ 2 9 4 6

_________________

(xi)

Th H T O

5 9 8 9

+ 2 3 6 4

_________________

(xii)

Th H T O

2 9 6 7

+ 5 4 6 9

_________________

(xiii)

Th H T O

3 7 5 7

+ 4 4 5 5

_________________

(xiv)

Th H T O

2 4 6 2

+ 3 7 8 9

_________________

(xv)

Th H T O

3 9 2 2

+ 2 5 5

+ 2 5

_________________

(xvi)

Th H T O

4 7 3 6

+ 3 2 4

+ 6 2

_________________

(xvii)

Th H T O

5 3 8 9

+ 8 2 5

+ 5 4

_________________

(xviii)

Th H T O

6 2 5 7

+ 9 4 7

+ 6 3`

_________________

(xix)

Th H T O

2 3 1 7

+ 2 6 7 4

+ 2 4 3

_________________

(xx)

Th H T O

1 6 7 8

+ 6 2 4 4

+ 5 7 5

_________________

(xxi)

Th H T O

1 9 3 6

+ 6 5 0 7

+ 3 8 5

_________________

(xxii)

Th H T O

2 4 5 8

+ 3 3 6 8

+ 4 5 2

_________________

(xxiii)

Th H T O

1 9 8 0

+ 2 0 5 5

+ 4 8 5 7

_________________

(xxiv)

Th H T O

2 8 7 5

+ 3 0 4 0

+ 1 9 3 5

_________________

(xxv)

Th H T O

1 6 8 0

+ 3 0 7 1

+ 2 8 2 9

_________________

(xxvi)

Th H T O

3 6 9 6

+ 1 4 8 6

+ 2 3 0 0

_________________

(xxvii)

Th H T O

1 3 5 4

+ 1 2 4 3

+ 3 4 4 3

+ 2 3 2 5

_________________

(xxviii)

Th H T O

2 5 6 4

+ 1 2 3 4

+ 1 0 2 4

+ 3 7 3 4

_________________

(xxviii)

Th H T O

2 4 3 6

+ 1 1 2 5

+ 1 3 4 4

+ 2 5 1 3

_________________

(xxx)

Th H T O

2 0 5 7

+ 2 7 4 0

+ 2 3 0 6

+ 1 4 7 5

_________________

Answer:

VII:

VIII: Do these Addition of 4-Digit Numbers with Regrouping Ones, Tens and Hundreds - sums in your Notebook:

(i) 6234 + 122 + 733 + 14

(ii) 5537 + 221 + 632 + 12

(iii) 7189 + 1234 + 567 + 64

(iv) 2764 + 6549 + 23 + 5

IX. Add the following 4-Digit Numbers With and Without Regrouping:

(i) 8 5 3 2

+ 1 3 4 6

_________

(ii) 5 1 4 2

+ 1 2 0 3

+ 2 6 3 1

__________

(iii) 2222 + 2222 + 2222 + 2222

(iv) 4926 + 5066

(v) 6523 + 1254 + 216

(vi) 3333 + 123 + 2113 + 2123

(vii) 6475 + 3328

(viii) 5636 + 154 + 2136

(ix) 4234 + 2234 + 2243 + 243

(x) 3547 + 2767

(xi) 7846 + 268 + 432

(xii) 5235 + 454 + 1234 + 2443

Answers:

IX. (i) 9878

(ii) 8976

(iii) 8888

(iv) 9992

(v) 7993

(vi) 7692

(vii) 9803

(viii) 7926

(ix) 8954

(x) 6314

(xi) 8546

(xii) 9366

X. Solve these 4-digit sums in your notebook:

(i) 2335 + 132

(ii) 2617 + 5250

(iii) 3624 + 5342

(iv) 2539 + 3270

(v) 1660 + 3282

(vi) 4771 + 2171

(vii) 3757 + 4455 + 2163

(viii) 3642 + 1212 + 2123

(ix) 2315 + 2222 + 2461

(x) 6352 + 221 + 23 + 388

(xi) 3214 + 2441 + 2223

(xii) 2315 + 2313 + 231

Answer:

X. (i) 2467

(ii) 7867

(iii) 8966

(iv) 5809

(v) 4942

(vi) 6942

(vii) 10375

(viii) 6977

(ix) 6998

(x) 6984

(xi) 7878

(xii) 4859

XI. Tick the correct options:

(i) The sum of 1456 + 1232 is -

(a) 5986

(b) 2688

(d) 8910

(ii) The sum of 7324 + 1456 is -

(a) 7556

(b) 3504

(d) 8780

(iii) The sum of 1270 + 1234 + 5086 is -

(a) 7590

(b) 3814

(d) 3172

(iv) The sum of 1421 + 612 + 2131 + 2256 is __________

(a) 8045

(b) 5218

(d) 5991

(v) (1150 + 5003) + 3312 = __________

(a) 1159

(b) 9465

(d) 4569

(vi) When we add 0 to a number, the sum is the __________

(a) 1

(b) 0

(d) none of these

(vii) In a particular year a batsman scored 4029 runs in ODI's and 2948 runs in Test matches. How many runs did he score altogether?

(a) 1577

(b) 1677

(d) 6977

Answer

XI. (i) → (b) 2688

(ii) → (d) 8780

(iii) → (a) 7590

(iv) → (c) 6420

(v) → (b) 9465

(vi) → (c) number itself

(vii) → (d) 6977

XII. Solve these 4-digit Addition Word Problems in your Note Book.

1. A company sold 4272 cars in January and 3517 cars in February. How many cars did the company sell in these months?

2. Ron bought bicycle for $ 2615 and television for $7138. How much did he spend?

3. A book contains 1198 pages and book contains 1374 pages. How many pages do both books contain altogether?

4. Ron earned $2583 in December, $3776 in January and $3456 in February. How much did he earn in these months?

5. In March, a mobile store sold 3693 touch screen, 4379 qwerty pad, 587 slider and 1168 smart phones. Find the total phones sold in March.

Answer:

XII. 1. 7789

2. 9753

3. 2572

4. 9815

5. 9827

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