Here we will learn subtracting 2-digit numbers with borrowing. The subtractions with borrowing are solved step-by-step in four different ways.
When we need to subtract bigger number from a smaller number in ones place, we regroup tens into ones.
Regrouping
We can write a 2-digit number in different ways by regrouping tens and ones.
16 can be written as
23 can be written as
Let us understand this with the help of an example.
A shopkeeper sells bananas. He has 6 bunches of 10's and 5 single bananas.
Nairitee wants to buy 37 bananas from the shopkeeper. The shopkeeper gives her 3 bunches of 10's and breaks one bunch of 10's to give 7 bananas.
The shopkeeper is now left with how many bananas?
Column Method
Arrange the numbers in columns and subtract. In ones place, 5 is smaller than 7. We cannot take away 7 from 5. So, we break one ten into 10 ones. Now we have, 15 ones in ones place and 5 tens in tens place.
15 ones - 7 ones = 8 We write 8 in ones place. Subtract 3 tens from 5 tens. 5 tens - 3 tens = 2 tens Write 2 in tens place. |
So, 65 - 37 = 28
Worked-out examples on subtracting 2-digit numbers with borrowing:
1. Subtract 9 from 15.
Solution:
T O
1 5
- 9
Since, 5 < 9, so 9 cannot be subtracted from 5. So, 1 ten, i.e., 10 ones is borrowed from the digit 1 of tens place. Now one ten, i.e., 10 ones are added to 5 ones to make it 15 ones. Now 15 ones – 9 ones = 6 ones.
Therefore, 15 – 9 = 6
2. Subtract 37
from 65
Solution:
The numbers are placed in column form, with the smaller number 37 written under the greater number 65.
T O
1 T → 10
6 5
- 3 7
2 8
(i) first ones are subtracted as 5 < 7 or 7 > 5. So, 7 cannot be subtracted from 5.
(ii) Now 1 ten is borrowed from 6 tens leaving 5 tens there.
(iii) 1 ten = 10 ones. So, 10 ones are added to 5 ones making the sum 15 ones
(iv) 7 ones are subtracted from 15 ones i.e., 15 ones – 7 ones = 8 ones. This 8 is written in one’s column.
(v) Now tens are subtracted. At ten’s place there are 5 tens left. So 5 tens – 3 tens = 2 tens. So, 2 is written in ten’s column.
(vi) Therefore, 65 – 37 = 28.
3. Subtract 28 from 83
Solution:
The smaller number 28 is written under greater number 83 in column form and ones are subtracted first, then the tens.
T O
1 T → 10
8 3
- 2 8
5 5
(i) 3 < 8, so 1 ten, i.e., 10 ones are borrowed from 8 tens with 7tens remaining there.
(ii) Now, 1 ten + 3 = 10 + 3 = 13 ones. So, 13 ones – 8 ones = 5 ones.
(iii) 7 tens – 2 tens = 5 tens.
Therefore, 83 – 28 = 55
4. Subtract 69 from 92
Solution:
The smaller number 69 is written under greater number 92 in column form and ones are subtracted first, then the tens.
T O
1 T → 10
9 2
- 6 9
2 3
(i) 10 + 2 = 12; 12 O – 9 O = 3 O
(ii) 8 T – 6 T = 2 T
Therefore, 92 – 69 = 23
Subtraction with Borrowing:
5. Let us subtract 5 from 23.
Step I: Arrange the numbers into tens and ones. | |
Step II: We cannot subtract 5 from 3. So, borrow 1 ten from the tens column. 1 ten = 10 ones. Take these 10 ones to the ones column. This gives: 10 + 3 = 13 ones 13 – 5 = 8 | |
Step III: Subtract the tens. Now since we borrowed 1 ten, we are left with 1 ten in the tens column. |
Thus, 23 – 5 = 18
6. Let us subtract 37 from 53.
Step I: Arrange the numbers into tens and ones. | |
Step II: We cannot subtract 7 from 3. So, borrow 1 ten from the tens column. 1 ten = 10 ones. Take these 10 ones to the ones column. This gives: 10 + 3 = 13 ones 13 – 7 = 6 | |
Step III: Since we have borrowed 1 ten from 5 tens, we are left with 4 tens. Now subtract 3 tens from 4 tens. 4 – 3 = 1 |
Thus, 53 – 37 = 16
Questions and Answers on Subtracting 2-Digit Numbers with Borrowing (Regrouping):
1. Regrouping the tens and ones.
(i) |
24 = |
2 |
tens + |
4 |
ones = |
1 |
ten + |
14 |
ones |
(ii) |
57 = |
___ |
tens + |
___ |
ones = |
4 |
tens + |
___ |
ones |
(iii) |
64 = |
___ |
tens + |
___ |
ones = |
___ |
tens + |
14 |
ones |
(iv) |
48 = |
___ |
tens + |
___ |
ones = |
3 |
tens + |
___ |
ones |
2. Subtracting 1-digit number from 2-digit number with regrouping.
(i) 38 - 9 = _____
(ii) 62 - 7 = _____
(iii) 44 - 6 = _____
(iv) 67 - 8 = _____
(v) 75 - 7 = _____
(vi) 94 - 8 = _____
(vii) 74 - 5 = _____
(viii) 51 - 2 = _____
(ix) 95 - 6 = _____
(x) 42 - 3 = _____
(xi) 53 - 4 = _____
(xii) 62 - 4 = _____
(xiii) 67 - 8 = _____
(xiv) 32 - 5 = _____
(xv) 22 - 9 = _____
(xvi) 93 - 3 = _____
Answers:
2. (i) 29
(ii) 55
(iii) 38
(iv) 59
(v) 68
(vi) 86
(vii) 69
(viii) 49
(ix) 89
(x) 39
(xi) 49
(xii) 58
(xiii) 59
(xiv) 27
(xv) 13
(xvi) 90
3. Subtracting 2-digit number with regrouping.
(i) 80 - 17 = _____
(ii) 38 - 29 = _____
(iii) 71 - 34 = _____
(iv) 47 - 19 = _____
(v) 86 - 27 = _____
(vi) 65 - 47 = _____
(vii) 51 - 25 = _____
(viii) 62 - 37 = _____
(ix) 73 - 57 = _____
(x) 94 - 46 = _____
(xi) 46 - 28 = _____
(xii) 56 - 27 = _____
(xiii) 57 - 19 = _____
(xiv) 31 - 24 = _____
(xv) 41 - 16 = _____
(xvi) 53 - 29 = _____
Answers:
3. (i) 63
(ii) 9
(iii) 37
(iv) 28
(v) 59
(vi) 18
(vii) 26
(viii) 25
(ix) 16
(x) 48
(xi) 18
(xii) 29
(xiii) 38
(xiv) 7
(xv) 25
(xvi) 24
4. Subtract.
(i) |
- |
T O 6 3 4 6 __________ |
(ii) |
- |
T O 3 4 2 9 __________ |
(iii) |
- |
T O 9 3 5 8 __________ |
(iv) |
- |
T O 7 6 5 9 __________ |
(v) |
- |
T O 3 2 1 5 __________ |
(vi) |
- |
T O 4 4 3 6 __________ |
(vii) |
- |
T O 5 2 2 8 __________ |
(viii) |
- |
T O 3 2 1 9 __________ |
(ix) |
- |
T O 8 3 6 9 __________ |
(x) |
- |
T O 7 5 2 6 __________ |
Answers:
4. (i) 17
(ii) 5
(iii) 35
(iv) 17
(v) 17
(vi) 8
(vii) 24
(viii) 13
(ix) 14
(x) 49
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