Subtraction with Regrouping

We will learn subtraction 4-digit, 5-digit and 6-digit numbers with regrouping.

Subtraction of 4-digit numbers can be done in the same way as we do subtraction of smaller numbers. We first arrange the numbers one below the other in place value columns and then we start subtracting from the ones place and regroup, if required as shown in the following examples.

Solved Examples on Subtraction of 4-Digit Numbers with Regrouping:

1. Subtract 3958 from 7461.

Solution:

Step I: Arrange the numbers vertically.

Step II: Subtract the ones. Since 8 > 1, we cannot subtract 8 from 1. Regroup 6 tens and 1 one. Now, 6 tens + 1 one = 5 tens and 11 ones. 11 – 8 = 3 ones. Write 3 in ones column.

Step III: Subtract the tens. 5 tens – 5 tens = 0 tens. Write 0 in tens column.

Step IV: Subtract the hundreds. Since 9 > 4, we cannot subtract 9 from 4. Regroup 7 thousands and 4 hundreds as 6 thousands and 14 hundreds. 14 – 9 = 5 hundreds. Write 5 in hundreds column.

Step V: Subtract the thousands. 6 – 3 = 3 thousands. Write 3 in thousands column.


Subtraction with Regrouping

Thus, 7461 – 3958 = 3503.


2. Subtract 2947 from 8163

Solution:

Step I: Arrange the numbers in columns.

Th

H

T

O

8

1

6

3

-

2

9

7

4


 

 

 

 

 



Step II: Subtract the ones. Here 3 < 4, so regroup 6 tens 3 ones as 5 tens and 13 ones.

Th

H

T

O



5

13

8

1

6

3

-

2

9

7

4


 

 

 

 

 9



Step III: Subtract the tens. Here, 5 < 7, so regroup 1 hundred 6 tens as O hundreds and 15 tens.

Th

H

T

O

15

13


0

5


8

1

6

3

-

2

9

7

4


 

 

 

 9



Step IV: Subtract the hundreds. Here, 0 < 9. so regroup 8 thousands 0 hundreds as 7 thousand and 10 hundreds.

Th

H

T

O

7

10

15

13


0

5


8

1

6

3

-

2

9

7

4


 

 

 1

 9



V: Subtract the thousands.

Th

H

T

O

7

10

15

13


0

5


8

1

6

3

-

2

9

7

4


 

 5

 1

 9



Hence, 8163 - 2974 = 5189

(Five thousand, one hundred eighty-nine.



3. Subtract 9,000 from 6,124

Solution:

Step I: Arrange the numbers in columns.

Th

H

T

O

9

0

0

0

-

6

1

2

4


 

 

 

 

 



Step II: Regroup 9 thousands.

9 thousands = 8 thousands + 10 hundreds.

10 hundreds = 9 hundreds + 10 tens.

10 tens = 9 tens + 10 ones.

Th

H

T

O

8

9

9

10


10

10


9

0

0

0

-

6

1

2

4


  

  

  

  

  



Step III: Subtract the ones.

Th

H

T

O

8

9

9

10


10

10


9

0

0

0

-

6

1

2

4


  

  

  

  



Step IV: Subtract the tens.

Th

H

T

O

8

9

9

10


10

10


9

0

0

0

-

6

1

2

4


  

  

  



Step V: Subtract the hundreds.

Th

H

T

O

8

9

9

10


10

10


9

0

0

0

-

6

1

2

4


  

  

8



Step VI: Subtract the hundreds.

Th

H

T

O

8

9

9

10


10

10


9

0

0

0

-

6

1

2

4


  

2

8


Hence, 9,000 - 6,124 = 2,876. (Two thousand eight hundred seventy-six)


Solved Examples on Subtraction of 5-Digit Numbers with Regrouping:

4. Subtract 28539 from 84248.

Solution:

Step I: Subtract ones. We cannot subtract 9 from 8. Borrow 1 ten from 4 tens. 1 ten = 10 ones. 10 + 8 = 18. 18 – 9 = 9. Write 9 under ones.

Step II: Subtract tens. 4 – 1 = 3 remains in the tens column. 3 – 3 = 0. Write 0 under tens.

Step III: Subtract hundreds. We cannot subtract 5 from 2. Borrow 1 thousand from 4 thousands. 1 thousand = 10 hundreds. 10 + 2 = 12 hundreds. 12 – 5 = 7. Write 7 under hundreds.

Step IV: Subtract thousands. 4 – 1 = 3 remains in the thousands column. 8 cannot be subtracted from 3. Borrow 1 ten thousand from 8 ten thousands. 1 ten thousand = 10 thousands. 10 + 3 = 13 thousands. 13 – 8 = 5. Write 5 under thousands.

Step V: Subtract ten thousands. 8 – 1 = 7 remains in the ten thousands column. 7 – 2 = 5. Write 5 under ten thousands.

Subtraction of 5-Digit Numbers with Regrouping

Therefore, the difference is 55709.


5. Subtract: 67,029 from 98,020.

TTh

Th

H

T

O

7

9

11

10

10

1

9

8

0

2

0

-

6

7

0

2

9



3

0

9

9

1


Therefore, 98,020 - 67,029 = 30,991


Solved Examples on Subtraction of 6-Digit Numbers with Regrouping:

6. Subtract 356993 from 734261

Solution:

Step I: Subtract ones. We cannot subtract 3 from 1. Borrow 1 ten from 6 tens. 1 ten = 10 ones. 10 + 1 = 11. 11 – 3 = 8. Write 8 under ones.

Step II: Subtract tens. 6 – 1 = 5 remains in the tens column. 9 cannot be subtracted from 5. Borrow 1 hundred from 2 hundreds. 1 hundred = 10 tens. 10 + 5 = 15. 15 – 9 = 6. Write 6 under tens.

Step III: Subtract hundreds. 2 – 1 = 1 remains in the hundreds column. 9 cannot be subtracted from 1. Borrow 1 thousand from 4 thousands. 1 thousand = 10 hundreds. 10 + 1 = 11 hundreds. 11- 9 = 2. Write 2 under hundreds.

Step IV: Subtract thousands. 4 – 1 = 3 remains in the thousands column. 6 cannot be subtracted from 3. Borrow 1 ten thousand from 8 ten thousands. 1 ten thousand = 10 thousands. 10 + 3 = 13 thousands. 13 – 6 = 7. Write 7 under thousands.

Step V: Subtract ten thousands. 3 – 1 = 2 remains in the ten thousands column. 5 cannot be subtracted from 2. Borrow 1 lakh from 7 lakhs. 1 lakh = 10 ten thousands. 10 + 2 = 12. 12 – 5 = 7. Write 7 under ten thousands.

Step V: Subtract lakhs. 7 – 1 = 6 remains in the lakhs column. 6 – 3 = 3. Write 3 under lakhs.

Subtraction of 6-Digit Numbers with Regrouping

Therefore, the difference is 377268.


7. Fill in the missing digits in the boxes:

We can find missing digits using addition and subtraction.

Subtraction with Regrouping

Solution:

Steps I: Add the difference to the minuend to get the subtrahend. 3 + 6 = 9

Step II: Subtract the difference from subtrahend to get the minuend. 5 – 4 = 1

4-Digit Subtraction with Regrouping

Word Problems on Subtraction with Regrouping:

1. The sum of two numbers is 58,729. One number is 19,556. What is the other number?

Solution:

Sum of the two numbers   = 58,729

One number                    = 19,556

The other number            = 58729 – 19556

                                      = 39,173

Therefore, the other number is 39173


Word Problems on 5-Digit Subtraction


Worksheet on Subtraction without Regrouping:

I. Find the difference:

(i) 6581 – 2339

(ii) 6467 – 4278

(iii) 7863 – 4790

(iv) 8800 – 5769

(v) 8810 – 6790

(vi) 2435 – 1692

(vii) 9000 – 7299

(viii) 3954 – 3874

(ix) 4964 – 3978

(x) 5007 – 4829

(xi) 4601 – 3709

(xii) 8841 – 7961


Answer:

1. (i) 4242

(ii) 2189

(iii) 3073

(iv) 3031

(v) 2020

(vi) 743

(vii) 1701

(viii) 80

(ix) 986

(x) 178

(xi) 892

(xii) 880


II. Subtract the following:

(i)      5  7  4  9  6  5

      –  5  4  3  2  2  7 

      ______________


(ii)     6 6 5 4 5 2

      – 3 7 4 5 9 2 

    ____________


(iii)     5 3 4 5 6

       – 4 9 3 2 4 

      __________

(iv)     8 6 2 4 1 7 0

       – 5 8 2 6 1 4 2 

       ____________

Answer:

II. (i) 31738

(ii) 290860

(iii) 4132

(iv) 2798028


III. Fill in the blanks:

(i) The predecessor of 8145 is ……………………

(ii) 1000 less than 6982 is ……………………

(iii) When 500 is taken from 7687, we get ……………………

(iv) When we subtract 2100 from 4598, we get ……………………

(v) Reducing 3500 from 7000 given us ……………………

(vi) Taking away 2222 from 3456 leaves ……………………

(vii) If we add 50 and 300 and subtract it from 6854, we get ……………………

(viii) …………………… - 501 = 500


Answer:

III. (i) 8144

(ii) 5982

(iii) 7187

(iv) 2498

(v) 3500

(vi) 1234

(vii) 6504

(viii) 1001


IV. Find the missing numbers in the following:

Find the Missing Numbers


Answer:

IV.

Find the Missing Numbers in 4-Digit Subtraction


V. Find the difference between:

(i) 7000 - 5409

(ii) 6845 and 4319

(iii) 3225 and 1084

(iv) 2965 and 3001

(v) 7486 and 9241

(vi) 6810 and 3920


Answer:

V. (i) 1591

(ii) 2526

(iii) 2141

(iv) 36

(v) 1455

(vi) 2890


VI. Find the difference between the largest 5-digit number and the smallest 6-digit number.


Answer:

VI. 1


VII. Find the number.

(i) 2550 less than 36,280

(ii) 5420 less than 4,57,275


Answer:

VII. (i) 33730


VIII. What must be added to 13901 to get 29345?

(Hint: Subtract 13901 from 29345)


Answer:

VIII. 15444


IX. Subtract the sum of 11998 and 3479 from 31970.


Answer:

IX. 16493


X. Find the difference.

(i) 8 thousands – 16 tens

(ii) 15 thousands – 12 hundreds

(iii) 2 ten thousands – 126 hundreds.


Answer:

X. (i) 7840

(ii) 13800

(iii) 7400


XI. Arrange in columns and subtract:

(i) 76,534 - 3,1654

(ii) 31,471 - 1,2042

(iii) 3,673 - 2,285

(iv) 7,0000 - 5,3212

(v) 4,500 - 2,637

(vi) 9,031 - 3,825


Answer:

XI. (i) 44,880

(ii) 19,429

(iii) 1,388

(iv) 16,788

(v) 1,863

(vi) 5,206


XII. Find the difference between:

(i) 28,653 and 13,430

(ii) 17,281 and 13,530

(iii) 36,197 and 14,200

(iv) 7,0000 and 3,5470

(v) 16,400 and 18,291

(vi) 48,092 and 25,174


Answer:

XII. (i) 15,223

(ii) 3,751

(iii) 21,997

(iv) 34,530

(v) 1,891

(vi) 22,918

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