We will learn about the subtraction of 4-digit numbers (without borrowing and with borrowing).
We know when one number is subtracted from another number the result obtained is called the difference. The greater number is called the minuend and the smaller number is called the subtrahend. We use subtraction when we take away, compare, to find out what does not belong to a group.
The rules of subtraction remain the same as for the number having less digits. We first write the greater number at the top. Then subtract the digits column-wise ones from ones, tens from tens, hundreds from hundreds, thousands from thousands and so on.
I. Subtraction of 4-Digit Numbers (without borrowing):
Consider some of the following examples.
1. Subtract 3276 from 5896.
Solution:
Th H T O
5 8 9 6
- 3 2 7 6 0 |
Subtract ones i.e., 6 - 6 = 0 and write down 0 in ones column. |
Th H T O
5 8 9 6
- 3 2 7 6 2 0 |
Subtract tens i.e., 9 - 7 = 2 and write down 2 in tens column. |
Th H T O
5 8 9 6
- 3 2 7 6 6 2 0 |
Subtract hundreds i.e., 8 - 2 = 6 and write down 6 in hundreds column. |
Th H T O 5 8 9 6
- 3 2 7 6
2 6 2 0 |
Subtract thousands i.e., 5 - 3 = 2 and write down 2 in thousands column. |
So the difference between 5896 and 3276 is 2620.
3. Subtract 2435 from 6769.
Solution:
Step I: Arrange the number in coloumn of thousands, hundreds, tens and ones.
Step II: Subtract ones.
Step III: Subtract tens.
Step IV: Subtract hundreds.
Step V: Subtract thousands.
4. Subtract 3573 from 7998.
Solution:
Th H T O
7 9 9 8
- 3 5 7 3
4 4 2 5
II. Subtraction of 4-Digit Numbers (with borrowing):
Subtraction with Regrouping:
Regrouping From Tens to Ones Place -
1. Subtract 4539 from 7968.
Th H T O 5 18 7 9 - 4 5 3 9 9 |
Subtracting Ones: 8 - 9 is not possible Regrouping 1 ten as 10 ones Borrow 1 ten make 18 Then 18 - 9 = 9 Write 9 under O. |
Th H T O 5 18 7 9 - 4 5 3 9 3 4 2 9 |
Subtracting Tens: Instead of 6 tens, we have 5 tens write 5 in tens place instead of 6 5 - 3 = 2 Write 2 under T. |
III. Subtraction of 4-Digit Numbers (with borrowing):
Subtraction with Regrouping:
Regrouping From Tens and Hundreds Place -
1. Subtract 6289 from 8675.
Th H T O 6 15 8 6 - 6 2 8 9 6 |
Subtracting Ones: 5 - 9 is not possible Regrouping 1 ten as 10 ones Borrow 1 ten make 15 Then 15 - 9 = 6 Write 9 under O. |
Th H T O 16 5 6 15 8 - 6 2 8 9 8 6 |
Subtracting Tens: Instead of 7 tens, we have 6 tens 6 - 8 is not possible. Regrouping 1 hundred as 10 tens borrow 1 hundred make 16 Then 16 - 8 = 8 Write 8 under T. |
Th H T O 16 5 6 15 8 - 6 2 8 9 3 8 6 |
Subtracting Hundreds: Instead of 6 hundreds, we have 5 hundreds Write 5 in hundreds place, instead of 6 Then 5 - 2 = 3 Write 3 under H. |
Th H T O 5 16 5 6 15 8 - 6 2 8 9 2 3 8 6 |
Subtracting Thousands: 8 - 6 = 2 Write 2 under Th. |
IV. Subtraction of 4-Digit Numbers (with borrowing):
Subtraction with Regrouping:
Regrouping From Tens, Hundreds and Thousands Place -
1. Subtract 3837 from 6825.
Th H T O 1 15 6 8 - 3 8 3 7 8 |
Subtracting Ones: 5 - 7 is not possible Regrouping 1 ten as 10 ones Borrow 1 ten make 15 Then 15 - 7 = 8 Write 8 under O. |
Th H T O 11 7 1 15 6 - 3 8 3 7 8 8 |
Subtracting Tens: Instead of 2 tens, we have 1 tens 1 - 3 is not possible. Regrouping 1 hundred as 10 tens borrow 1 hundred make 11 Then 11 - 3 = 8 Write 8 under T. |
Th H T O 17 11 5 7 1 15 6 - 3 8 3 7 9 8 8 |
Subtracting Hundreds: Instead of 8 hundreds, we have 7 hundreds 7 - 8 is not possible. Regroup 1 thousand as 10 hundred Borrow 1 thousand make 17 Then 17 - 8 = 9 Write 9 under H. |
Th H T O 17 11 5 7 1 15 - 3 8 3 7 2 9 8 8 |
Subtracting Thousands: Instead of 6 thousands, we have 5 thousands 5 - 3 = 2 Write 2 under Th. |
Consider the following example.
2. Subtract 7864 from 9643.
Solution:
Th H T O
3 13 9 6 4 3
- 7 8 6 4 9 |
Subtract Ones: We cannot subtract 4 ones from 3 ones. So, we borrow 1 ten (1 ten and 3 ones become 13 ones). Now 13 ones - 4 ones = 9 ones. Write 9 in ones place. |
Th H T O
5 13
9 6 4 3 - 7 8 6 4 7 9 |
Subtract Tens: We cannot subtract 6 tens from 3 tens. So, we again borrow 1 hundred (1 hundred and 3 tens become 13 tens). Now 13 tens - 6 tens = 7 tens. Write 7 in tens place. |
Th H T O
8 15
9 6 4 3 - 7 8 6 4 7 7 9 |
Subtract Hundreds: We cannot subtract 8 hundreds from 5 hundreds. So, we again borrow 1 thousand (1 thousand and 5 hundreds become 15 hundreds). Now 15 hundreds - 8 hundreds = 7 hundreds. Write 7 in hundreds place. |
Th H T O
8
9 6 4 3 - 7 8 6 4 1 7 7 9 |
Subtract Thousands: We can subtract 7 thousands from 8 thousands i.e., 8 thousands - 7 thousands = 1 thousands. Write 1 in thousands place. |
So, the difference between 9643 and 7864 is 1779.
Questions and Answers on Subtraction of 4-Digit Numbers:
1. Solve the following of 4-digit Subtraction (Without Borrowing):
(i) Th H T O 3 3 8 9 - 2 4 3 _________________ |
(ii) Th H T O 8 5 6 7 - 3 4 5 _________________ |
(iii) Th H T O 6 5 7 4 - 1 5 2 _________________ |
(iv) Th H T O 5 8 9 9 - 6 7 6 _________________ |
(v) Th H T O 4 4 5 2 - 1 3 1 _________________ |
(vi) Th H T O 8 7 4 6 - 5 5 3 4 _________________ |
(vii) Th H T O 7 6 5 6 - 3 4 2 4 _________________ |
(viii) Th H T O 5 8 8 6 - 2 5 5 3 _________________ |
(ix) Th H T O 9 7 9 8 - 5 5 7 6 _________________ |
(x) Th H T O 8 6 5 4 - 4 6 5 4 _________________ |
(xi) Th H T O 7 7 7 7 - 5 4 3 2 _________________ |
(xii) Th H T O 6 9 7 6 - 3 6 4 1 _________________ |
(xiii) Th H T O 3 8 7 9 - 1 5 6 8 _________________ |
(xiv) Th H T O 4 4 4 4 - 2 1 3 2 _________________ |
(xv) Th H T O 9 9 8 8 - 5 6 3 4 _________________ |
(xvi) Th H T O 4 5 7 9 - 2 3 1 5 _________________ |
(xvii) Th H T O 5 6 9 2 - 3 4 8 1 _________________ |
(xviii) Th H T O 6 8 3 2 - 2 2 0 1 _________________ |
(xix) Th H T O 7 5 6 4 - 3 1 2 1 _________________ |
(xx) Th H T O 9 9 6 5 - 8 6 1 3 _________________ |
(xxi) Th H T O 7 4 3 7 - 5 4 3 6 _________________ |
(xxii) Th H T O 2 1 4 1 - 1 0 2 0 _________________ |
(xxiii) Th H T O 8 7 6 5 - 4 4 2 3 _________________ |
(xxiv) Th H T O 9 8 7 6 - 8 7 6 5 _________________ |
(xxv) Th H T O 5 6 7 8 - 2 3 4 5 _________________ |
2. Solve the following of 4-digit Subtraction (Without Borrowing):
(i) Th H T O 9 9 8 6 - 8 6 5 _________________ |
(ii) Th H T O 8 6 8 7 - 3 2 4 _________________ |
(iii) Th H T O 7 8 4 6 - 5 2 3 _________________ |
(iv) Th H T O 6 5 7 6 - 4 3 3 _________________ |
(v) Th H T O 5 7 9 8 - 5 2 3 _________________ |
(vi) Th H T O 8 7 8 6 - 5 2 5 2 _________________ |
(vii) Th H T O 2 4 6 8 - 1 2 3 5 _________________ |
(viii) Th H T O 6 8 5 4 - 3 4 2 2 _________________ |
(ix) Th H T O 7 9 6 4 - 4 5 1 2 _________________ |
(x) Th H T O 3 4 7 5 - 1 1 6 4 _________________ |
(xi) Th H T O 5 7 7 9 - 5 5 4 4 _________________ |
(xii) Th H T O 9 5 8 9 - 4 2 4 3 _________________ |
(xiii) Th H T O 4 2 9 4 - 3 1 6 3 _________________ |
(xiv) Th H T O 8 7 6 6 - 4 3 4 1 _________________ |
(xv) Th H T O 7 5 8 7 - 6 3 4 5 _________________ |
(xvi) Th H T O 4 2 2 3 - 2 1 1 2 _________________ |
(xvii) Th H T O 5 8 2 9 - 4 7 1 5 _________________ |
(xviii) Th H T O 9 9 9 9 - 7 7 7 7 _________________ |
(xix) Th H T O 6 6 9 7 - 4 5 7 5 _________________ |
(xx) Th H T O 8 9 9 8 - 5 7 7 4 _________________ |
3. Do these following of 4-Digit Subtraction (Without Borrowing) in your Notebook:
(i) 4679 - 1256
(ii) 2942 - 1621
(iii) 2687 - 432
(iv) 8975 - 853
(v) 3387 - 1264
(vi) 3778 - 2764
(vii) 6799 - 5678
(viii) 7832 - 3411
(ix) 6876 - 3354
(x) 9797 - 8546
(xi) 7000 - 1000
(xii) 9569 - 5217
(xiii) 5575 - 3343
(xiv) 4989 - 2545
(xv) 3957 - 1723
(xvi) 7586 - 6312
(xvii) 8657 - 1435
(xviii) 5569 - 2556
(xix) 9649 - 4535
(xx) 3456 - 1243
(xxi) 2685 - 1173
(xxii) 5867 - 4334
(xxiii) 4735 - 2312
(xiv) 6987 - 4546
4. Subtract the following Regrouping from Tens to Ones Place:
(i) Th H T O 1 3 4 7 - 2 9 _________________ |
(ii) Th H T O 4 7 5 5 - 3 6 _________________ |
(iii) Th H T O 8 7 6 4 - 3 7 _________________ |
(iv) Th H T O 1 6 7 5 - 4 8 _________________ |
(v) Th H T O 3 4 6 2 - 1 6 _________________ |
(vi) Th H T O 2 6 7 5 - 2 3 7 _________________ |
(vii) Th H T O 7 8 8 7 - 4 6 8 _________________ |
(viii) Th H T O 6 5 8 1 - 4 5 9 _________________ |
(ix) Th H T O 3 7 8 5 - 3 6 7 _________________ |
(x) Th H T O 4 6 5 4 - 1 2 6 _________________ |
(xi) Th H T O 7 8 5 4 - 2 4 3 7 _________________ |
(xii) Th H T O 9 5 6 1 - 7 3 1 7 _________________ |
(xiii) Th H T O 8 8 7 1 - 5 4 5 6 _________________ |
(xiv) Th H T O 5 3 2 6 - 2 1 1 7 _________________ |
(xv) Th H T O 6 7 8 3 - 3 5 6 7 _________________ |
(xvi) Th H T O 3 6 7 4 - 1 2 5 9 _________________ |
(xvii) Th H T O 4 5 8 3 - 1 2 1 6 _________________ |
(xviii) Th H T O 5 9 8 2 - 4 5 4 6 _________________ |
(xix) Th H T O 6 9 8 3 - 3 7 2 9 _________________ |
(xx) Th H T O 7 5 6 3 - 6 4 2 8 _________________ |
(xxi) Th H T O 9 8 7 6 - 7 6 5 9 _________________ |
(xxii) Th H T O 8 9 7 4 - 6 5 2 7 _________________ |
(xxiii) Th H T O 7 7 7 7 - 1 2 3 9 _________________ |
(xxiv) Th H T O 6 8 9 4 - 4 6 5 7 _________________ |
(xxv) Th H T O 5 4 8 2 - 3 2 6 3 _________________ |
5. Subtract the following Regrouping from Tens to Ones Place:
(i) Th H T O 3 7 8 5 - 4 7 _________________ |
(ii) Th H T O 7 6 4 6 - 2 7 _________________ |
(iii) Th H T O 4 5 8 3 - 4 8 _________________ |
(iv) Th H T O 6 3 5 2 - 3 5 _________________ |
(v) Th H T O 5 2 7 4 - 5 6 _________________ |
(vi) Th H T O 2 3 7 6 - 1 5 8 _________________ |
(vii) Th H T O 5 6 7 3 - 5 5 7 _________________ |
(viii) Th H T O 3 7 7 1 - 5 5 4 _________________ |
(ix) Th H T O 8 8 9 2 - 6 7 8 _________________ |
(x) Th H T O 9 9 6 5 - 8 3 6 _________________ |
(xi) Th H T O 6 6 9 2 - 2 3 7 5 _________________ |
(xii) Th H T O 9 8 7 6 - 5 4 3 7 _________________ |
(xiii) Th H T O 8 7 6 4 - 5 5 3 7 _________________ |
(xiv) Th H T O 7 7 8 7 - 4 5 6 8 _________________ |
(xv) Th H T O 4 7 5 3 - 3 6 2 5 _________________ |
(xvi) Th H T O 8 8 8 8 - 6 6 6 9 _________________ |
(xvii) Th H T O 7 6 5 4 - 5 2 2 8 _________________ |
(xviii) Th H T O 5 8 9 1 - 1 5 6 3 _________________ |
(xix) Th H T O 4 6 5 2 - 1 2 1 5 _________________ |
(xx) Th H T O 9 7 6 6 - 8 3 1 8 _________________ |
(xxi) Th H T O 7 6 9 4 - 5 2 7 8 _________________ |
(xxii) Th H T O 5 8 8 3 - 2 6 6 9 _________________ |
(xxiii) Th H T O 9 7 9 4 - 2 3 7 6 _________________ |
(xxiv) Th H T O 6 9 9 3 - 4 7 7 7 _________________ |
(xxv) Th H T O 4 6 9 2 - 1 3 8 9 _________________ |
6. Do these following 4-Digit Subtraction (Regrouping from Tens to Ones Place) Sums in your Notebook -
(i) 3778 - 1559
(ii) 5973 - 2769
(iii) 9788 - 9549
(iv) 3738 - 1419
(v) 5963 - 2735
(vi) 8746 - 5518
(vii) 5464 - 3245
(viii) 6455 - 2137
(ix) 6375 - 4158
(x) 8793 - 6676
(xi) 2872 - 1557
(xii) 8654 - 6326
(xiii) 5621 - 3212
(xiv) 8457 - 4239
(xv) 9356 - 7128
(xvi) 6562 - 1117
7. Subtract the following Regrouping from Tens and Hundreds Place:
(i) Th H T O 6 9 5 1 - 7 6 8 _________________ |
(ii) Th H T O 4 5 5 1 - 3 7 2 _________________ |
(iii) Th H T O 3 6 1 1 - 2 6 4 _________________ |
(iv) Th H T O 8 9 1 1 - 2 5 3 _________________ |
(v) Th H T O 2 7 4 7 - 5 8 9 _________________ |
(vi) Th H T O 4 2 2 3 - 1 3 2 _________________ |
(vii) Th H T O 3 5 5 4 - 4 6 5 _________________ |
(viii) Th H T O 2 6 3 3 - 3 8 5 _________________ |
(ix) Th H T O 4 6 1 4 - 4 3 5 _________________ |
(x) Th H T O 2 7 5 4 - 2 8 5 _________________ |
(xi) Th H T O 2 6 3 4 - 1 4 6 8 _________________ |
(xii) Th H T O 7 5 2 6 - 3 2 8 8 _________________ |
(xi) Th H T O 3 4 4 7 - 1 2 5 6 _________________ |
(xii) Th H T O 5 3 4 1 - 4 2 9 6 _________________ |
(xiii) Th H T O 6 6 6 6 - 4 5 7 8 _________________ |
(xiv) Th H T O 6 7 6 3 - 5 6 9 8 _________________ |
(xv) Th H T O 8 2 5 2 - 4 0 8 4 _________________ |
(xvi) Th H T O 7 9 2 6 - 5 1 4 8 _________________ |
(xv) Th H T O 9 5 4 7 - 8 3 9 8 _________________ |
(xvi) Th H T O 4 3 8 6 - 2 1 9 8 _________________ |
8. Subtract the following Regrouping from Tens and Hundreds Place:
(i) Th H T O 2 9 4 3 - 6 5 _________________ |
(ii) Th H T O 4 8 5 6 - 6 7 _________________ |
(iii) Th H T O 5 3 2 1 - 3 4 _________________ |
(iv) Th H T O 4 6 3 5 - 4 6 _________________ |
(v) Th H T O 2 8 2 5 - 3 7 _________________ |
(vi) Th H T O 5 9 4 5 - 4 5 6 _________________ |
(vii) Th H T O 6 8 1 4 - 6 2 8 _________________ |
(viii) Th H T O 7 6 4 3 - 3 6 5 _________________ |
(ix) Th H T O 8 4 3 2 - 1 4 6 _________________ |
(x) Th H T O 5 6 2 3 - 4 4 6 _________________ |
(xi) Th H T O 7 9 7 2 - 5 7 9 4 _________________ |
(xii) Th H T O 8 6 3 1 - 5 3 4 9 _________________ |
(xiii) Th H T O 9 7 2 5 - 7 5 3 7 _________________ |
(xiv) Th H T O 5 8 5 3 - 2 4 7 6 _________________ |
(xv) Th H T O 7 6 3 3 - 5 3 7 6 _________________ |
(xvi) Th H T O 9 6 5 6 - 5 3 8 7 _________________ |
(xvii) Th H T O 6 5 4 3 - 4 2 5 8 _________________ |
(xviii) Th H T O 3 9 1 5 - 1 5 3 7 _________________ |
(xix) Th H T O 5 4 2 7 - 3 2 6 9 _________________ |
(xx) Th H T O 6 7 4 1 - 4 3 7 9 _________________ |
(xxi) Th H T O 8 4 6 5 - 4 2 9 8 _________________ |
(xxii) Th H T O 9 6 3 3 - 5 1 4 5 _________________ |
(xxiii) Th H T O 6 4 1 3 - 5 2 4 8 _________________ |
(xxiv) Th H T O 3 4 2 1 - 1 1 4 5 _________________ |
(xxv) Th H T O 5 7 6 4 - 3 5 9 9 _________________ |
9. Subtract the following Regrouping from Tens and Hundreds Place:
(i) 4458 - 3798
(ii) 3452 - 276
(iii) 4450 - 337
(iv)8642 - 6156
(v) 7956 - 3478
(vi) 6953 - 2768
(vii) 4781 - 393
(viii) 6521 - 3443
(ix) 7832 - 6797
(x) 5423 - 2287
(xi) 8352 - 4187
(xii) 4572 - 289
(xiii) 7826 - 4377
(xiv) 7624 - 4356
(xv) 6783 - 2294
(xvi) 9740 - 6681
(xvii) 6345 - 289
(xviii) 1725 - 268
(xix) 6731 - 4482
(xx) 8642 - 6457
10. Subtract the following Regrouping From Tens, Hundreds and Thousands Place:
(i) Th H T O 2 3 2 5 - 4 3 7 _________________ |
(ii) Th H T O 3 2 2 5 - 4 4 7 _________________ |
(iii) Th H T O 4 1 1 2 - 4 3 6 _________________ |
(iv) Th H T O 5 1 5 7 - 2 6 8 _________________ |
(v) Th H T O 6 8 3 4 - 9 8 6 _________________ |
(vi) Th H T O 8 6 0 1 - 7 3 8 _________________ |
(vii) Th H T O 9 8 5 0 - 8 9 9 _________________ |
(viii) Th H T O 1 5 0 6 - 8 5 9 _________________ |
(ix) Th H T O 3 5 2 3 - 7 4 6 _________________ |
(x) Th H T O 6 5 3 3 - 9 4 4 _________________ |
(xi) Th H T O 6 2 8 2 - 3 8 9 5 _________________ |
(xii) Th H T O 4 3 2 8 - 2 5 8 9 _________________ |
(xiii) Th H T O 9 0 0 2 - 4 6 8 4 _________________ |
(xiv) Th H T O 8 3 4 3 - 2 6 8 4 _________________ |
(xv) Th H T O 8 4 3 4 - 4 8 4 6 _________________ |
(xvi) Th H T O 4 6 8 5 - 3 7 9 6 _________________ |
(xvii) Th H T O 6 1 2 3 - 3 2 6 9 _________________ |
(xviii) Th H T O 5 3 3 2 - 2 5 9 8 _________________ |
(xix) Th H T O 4 0 0 0 - 2 8 9 9 _________________ |
(xx) Th H T O 5 2 1 3 - 3 7 8 7 _________________ |
11. Subtract the following Regrouping From Tens, Hundreds and Thousands Place:
(i) Th H T O 6 2 8 3 - 7 9 4 _________________ |
(ii) Th H T O 5 4 8 8 - 6 9 9 _________________ |
(iii) Th H T O 8 6 4 2 - 7 5 4 _________________ |
(iv) Th H T O 7 3 5 7 - 8 9 8 _________________ |
(v) Th H T O 6 6 4 2 - 7 9 7 _________________ |
(vi) Th H T O 7 6 5 6 - 7 6 8 _________________ |
(vii) Th H T O 6 5 4 3 - 7 5 4 _________________ |
(viii) Th H T O 4 4 7 2 - 6 8 4 _________________ |
(ix) Th H T O 4 5 7 6 - 7 8 9 _________________ |
(x) Th H T O 2 4 5 2 - 5 8 4 _________________ |
(xi) Th H T O 8 7 8 1 - 4 9 9 6 _________________ |
(xii) Th H T O 4 3 8 7 - 2 6 9 6 _________________ |
(xiii) Th H T O 3 6 7 3 - 1 7 8 6 _________________ |
(xiv) Th H T O 2 4 4 2 - 1 6 6 5 _________________ |
(xv) Th H T O 6 9 8 8 - 5 9 9 9 _________________ |
(xvi) Th H T O 5 4 3 2 - 3 7 8 8 _________________ |
(xvii) Th H T O 5 3 4 4 - 1 4 6 6 _________________ |
(xviii) Th H T O 2 5 5 4 - 1 9 6 7 _________________ |
(xix) Th H T O 4 8 6 2 - 2 9 8 7 _________________ |
(xx) Th H T O 8 3 2 1 - 6 6 4 5 _________________ |
(xxi) Th H T O 3 8 8 8 - 1 9 9 9 _________________ |
(xxii) Th H T O 8 6 5 7 - 5 6 6 8 _________________ |
(xxiii) Th H T O 9 3 2 1 - 4 4 4 4 _________________ |
(xxiv) Th H T O 7 4 5 6 - 3 7 9 8 _________________ |
(xxv) Th H T O 6 4 5 3 - 2 7 6 5 _________________ |
12. Subtract the following Regrouping From Tens, Hundreds and Thousands Place:
(i) 8452 - 668
(ii) 1725 - 879
(iii) 3452 - 687
(iv) 9675 - 789
(v) 5367 - 989
(vi) 4781 - 893
(vii) 2345 - 567
(viii) 5432 - 3676
(ix) 7546 - 5678
(x) 8658 - 6779
(xi) 9568 - 4679
(xii) 9898 - 4899
(xiii) 7777 - 5888
(xiv) 4213 - 1654
(xv) 4423 - 3566
(xvi) 3214 - 1655
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