Subtracting 2-Digit Numbers

In subtracting 2-digit numbers we will subtract or minus a one-digit number from another two-digit number and a two-digit number from another two-digit number. To find the difference between the two numbers we need to ‘ones from ones’ and ‘tens from tens’.

Let us subtract 2 from 39

= 37 ones = 3 tens + 7 ones

Subtract ones and write in the ones place. 9 ones – 2 ones = 7 ones Subtract tens and write in the tens place. 3 tens – 0 tens = 3 tens

39 – 2 = 37

Let us subtract 34 from 65.

= 31 ones = 3 tens + 1 one

Subtract ones and write in the ones place. 5 ones – 4 ones = 1 ones Subtract tens and write in the tens place. 6 tens – 3 tens = 3 tens

65 – 34 = 31

How to subtract two digit numbers?

The steps of the examples on subtracting 2-digit numbers i.e. ‘ones from ones’ and ‘tens from tens’:

1. Subtract 41 from 63.

(i) First arrange the numbers vertically so that the tens' place digits and ones' place digits are lined up which means in simple one number should be written above the other number. Draw a line under the bottom number.

(ii) Subtract the digits in the ones place. Subtract (3 - 1 = 2). Place 2 in the ones column as shown.

(iii) Subtract the digits in the tens' place. Subtract (6 - 4 = 2). Place 2 in the tens column as shown.

(iv) The difference of 63 – 41 is 22

2. Subtract 52 from 86.

(i) First arrange the numbers vertically so that the tens' place digits and ones' place digits are lined up which means in simple one number should be written above the other number. Draw a line under the bottom number.

(ii) Subtract the digits in the ones place. Subtract (6 - 2 = 4). Place 4 in the ones column as shown.

(iii) Subtract the digits in the tens' place. Subtract (8 - 5 = 3). Place 3 in the tens column as shown.

(iv) The difference of 86 - 52 is 34

3. Subtract 42 from 78

Solution:

(i) Given numbers are written in column form. The greater number is written first, then the smaller number is written. (ii) First, the digits of one’s place are taken. 2 is subtracted from 8.  8 ones – 2 ones = 6 ones. This 6 is written in one’s column.              (iii) Now digits of tens place are written 4 is subtracted from 7.     7 tens – 4 tens = 3 tens. This 3 is written in tens column.

Hence, 78 - 42 = 36

4. Let us subtract 24 from 39.

Let us learn how to subtract 2-digit numbers using an abacus.

1. Subtract 26 from 49.

Step I: Look at the ones rod.

Take away 6 beads.

9 – 6 = 3

Step II: Look at the tens rod. Take away 2 beads. 4 – 2 = 2 We get the number 23. Thus, 49 – 26 = 23

2. Subtract 31 from 73.

Step I: Look at the ones rod.

Take away 1 bead.

3 – 1 = 2

Step II: Look at the tens rod. Take away 3 beads. 7 – 3 = 4 We get the number 42. Thus, 73 – 31 = 42

Note: To do subtraction using an abacus, first subtract the beads o the ones rod and then subtract the beads on the tens rod.

Subtraction of 2-Digit Numbers without Borrowing or without Regrouping:

1. Let us subtract 7 from 29.

Step I: Arrange the two numbers under tens and ones.

Step II: First subtract the ones.

Step III: Subtract the tens.

Thus, 29 – 7 = 22

2. Subtract 23 from 38.

Step I: Arrange the two numbers under tens and ones.

Step II: First subtract the ones.

Step III: Subtract the tens.

Thus, 38 – 23 = 15

● In subtraction there are three numbers as:

     95  ←   the number from which smaller number is subtracted is called minuend. 

  - 23   ←   the number to be subtracted is called the subtrahend.

    72   ←    the number which is the subtracted result is called the difference.

Here, in subtracting 2-digit numbers we get 95 is minuend, 23 is subtrahend and 72 is difference.

Minuend is always greater than subtrahend.

More Examples on Subtraction of Two Digit Numbers

1. Subtract 23 from 36.

     T  O

     3  6  = 3 tens + 6 ones   =  30 + 6

     2  3  = 2 tens + 3 ones   =  20 + 3

   -          -           -                 -     -     

     1  3  = 1 ten  + 3 ones   = 10 + 3     = 13

Method:

Step I: Subtract the ones,

6 ones - 3 ones = 3 ones.

Write 3 under the ones column.

Step II: Subtract the tens,

3 tens - 2 tens = 1 ten.

Write 1 under the tens column.

Therefore, 36 - 23 = 13

We can do the same problem in a short way

Short way:

                 T   O

                 3   6

             -   2   3

                 1   3            (Steps remain the same as above)

2. Subtract 23 from 36.

                 T   O

                 7   8

             -   3   2

                 4   6  

Method:

Step I: Subtract the ones,

8 ones - 2 ones = 6 ones.

Write 6 under the ones column.

Step II: Subtract the tens,

7 tens - 3 tens = 4 tens.

Write 4 under the tens column.

Therefore, 78 - 32 = 46

3. Anthony had 55 crayons. He gave 21 to his friend. How many crayons were left with Anthony?

55 - 21 = ?

Step I: First subtract the ones.

5 - 1 = 4 ones

Write 4 under ones column.

Step II: Next, subtract the tens.

5 - 2 = 3

Write 3 under tens.

So, 34 crayons left with Anthony.

4. Let us subtract 12 from 75.

Write the numbers one below the other as shown.

Always write the greater number above the smaller number.

Step I: Subtract the ones.

           5 ones - 2 ones = 3 ones

           Write 3 in the ones place.

Step II: Subtract the tens.

             7 tens - 1 ten = 6 tens

             Write 6 in the tens place.

The difference is 63.

Subtraction of 2-Digit Numbers with Borrowing or with Regrouping:

Sometimes we have to borrow the digits as we borrow things.

Regrouping

Sometimes the digit we need to subtract is bigger than the digit it has to be subtracted from. In such a case we regroup or borrow from the digit at the higher place.

Let us first learn regrouping.

34 is same as 3 tens and 4 ones

Let us understand.

1. Nancy has 42 stickers. She pasted 15 stickers in her album. How many stickers yet to be pasted?

42 - 15 = ?

Step I: Since we cannot subtract 5 ones from 2 ones, so borrowing from tens is needed.

So, borrow 1 ten from tens column.

1 ten + 2 ones = 12 ones.

Now, subtract ones. 12 - 5 = 7 ones.

Write 7 in the ones place.

Step 2: In tens column,

we are left with 3 tens.

Subtract tens. 3 - 1 = 2 tens.

Write 2 in the tens place.

So, 27 stickers yet to be pasted.

Subtraction of 2-digit Numbers with Regrouping:

Note: In subtraction regrouping is also known as borrowing.

2. Let us subtract (take away) 16 from 42.

Start by subtracting the ones. But we cannot take away 6 ones from 2 ones. So, we regroup 42 by opening one bundle of 10 matchsticks. Now, we have 12 ones.

Take away 6 ones from 12 ones. 6 ones are left.

Next, subtract the tens. Take away 1 ten from 3 tens (remaining). 2 tens are left.

The difference is 26.

3. Subtract by regrouping.

(i) 31 - 24 = _____

(ii) 55 - 18 = _____

4. Now, let us subtract 16 from 42 the short way.

Write the numbers one below the other as shown.

Step I: Subtract the ones. But 6 ones cannot be taken away from 2 ones.

So, borrow 1 ten from 4 tens.

We are left with 3 tens. Cross out 4 and write 3.

Regroup: 1 ten (borrowed) with 2 ones = 12 ones

12 ones - 6 ones = 6 ones

Write 6 in the ones place.

Step II: Subtract the tens.

3 tens (remaining) - 1 ten = 2 tens

Write 2 in the tens place.

The difference is 26.

Some Facts about Subtraction:

1. When we subtract 0 from a number, the difference is the number itself. For example, 25 - 0 = 25

2. When we subtract a number from itself, the difference is 0. For example, 25 - 25 = 0

3. When we subtract 1 from a number, the difference is the predecessor of that number, For example, 25 - 1 = 24 (24 is the predecessor of 25)

Worksheet on Subtracting 2-Digit Numbers:

1. Subtract the following:

(i) 60 - 10 = _____

(ii) 58 - 13 = _____

(iii) 88 - 33 = _____

(iv) 62 - 41 = _____

(v) 43 - 21 = _____

(vi) 57 - 26 = _____

(vii) 72 - 61 = _____

(viii) 47 - 11 = _____

(ix) 97 - 45 = _____

(x) 38 - 26 = _____

(xi) 71 - 60 = _____

(xii) 25 - 14 = _____

(xiii) 63 - 32 = _____

(xiv) 59 - 20 = _____

(xv) 37 - 12 = _____

(xvi) 89 - 69 = _____

2. Find the difference of the following 2-digit numbers without regrouping:

3. Find the difference of the following 2-digit numbers with regrouping:

Answer:

1. (i) 50

(ii) 45

(iii) 55

(iv) 21

(v) 22

(vi) 31

(vii) 11

(viii) 36

(ix) 52

(x) 12

(xi) 11

(xii) 11

(xiii) 31

(xiv) 39

(xv) 25

(xvi) 20

2. (i) 11

(ii) 34

(iii) 52

(iv) 63

(v) 22

(vi) 41

(vii) 40

(viii) 61

(ix) 33

(x) 31

(xi) 32

(xii) 40

(xiii) 25

(xiv) 35

(xv) 41

(xvi) 20

(xvii) 25

(xviii) 70

(xix) 50

(xx) 12

(xxi) 23

(xxii) 16

(xxiii) 25

(xxiv) 23

(xxv) 21

(xxvi) 23

3. (i) 69

(ii) 34

(iii) 19

(iv) 88

(v) 29

(vi) 45

(vii) 8

(viii) 45

(ix) 48

(x) 32

(xi) 29

(xii) 68

(xiii) 19

(xiv) 43

(xv) 44

(xvi) 46

(xvii) 15

(xviii) 59

(xix) 27

(xx) 7

(xxi) 4

(xxii) 59

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