# Adding 2-Digit Numbers

Here we will learn adding 2-digit numbers without regrouping and start working with easy numbers to get acquainted with the addition of two numbers.

We are going to start working with the basic addition of two-digits with everything arranged because this is what we will always do with bigger numbers in future.

Addition of 2-digit Numbers

Let us learn how to add 2-digit numbers

Addition of 2-digit Numbers Using an Abacus:

For example:

1. Let us add 31 and 27 using an abacus.

 Step 1: Put the ones beads together. 1    +    7    =    8 Step 2: Put the tens beads together. 3    +    2    =    5We get the number 58.

Thus, 31 + 27 = 58

2. Let us add 45 and 50 using an abacus.

 Step 1: Put the ones beads together. 5 + 0 = 5 Step 2: Put the tens beads together. 4 + 5 = 9We get the number 95.

Thus, 45 + 50 = 95

How to add two two-digit numbers without carrying?

Let’s follow the steps and start learning adding 2-digit numbers without regrouping with the help of an example.

1. Let us add 22 and 36.

 Step I: Write each digit of numbers in place value columns.
 Step II: (i) Add the ones and write in the once place.2 ones + 6 ones = 8 ones.(ii) Add the tens and write in the tens place.2 tens + 3 tens = 5 tens.

Answer: 22 + 36 = 58

2. Let us add 72 and 2.

First add the ones and then the tens.

Thus, 72 + 2 = 74

3. Let us add 32 and 27.

Step 1: Arrange the numbers in tens and ones.

 Step 2: Add the ones. Step 3: Add the tens.

Thus, 32 + 27 = 59

4. 26 + 41

(i) 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) Add first the ones' place digits. (6 + 1 = 7).

(iii) Then add the tens' place digits. (2 + 4 = 6).

(iv) The answer of 26 + 41 = 67.

Method II: 26 + 41

26          =           2 tens + 6 unit → addend

+ 41          =           4 tens + 1 unit → addend

67          =           6 tens + 7 unit → sum

So, adding 26 + 41 = 67.

Follow the steps of another example of adding 2-digit numbers.

5. 53 + 32

(i) 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) Add first the ones' place digits. (3 + 2 = 5).

(iii) Then add the tens' place digits. (5 + 3 = 8).

(iv) The answer of 53 + 32 = 85.

Method II: 53 + 32

53          =           5 tens + 3 unit → addend

+ 32          =           3 tens + 2 unit → addend

85          =           8 tens + 5 unit → sum

So, adding 53 + 32 = 85.

Addition of Two Digit Numbers

6. Add 32 and 53

3 2     =  3 tens + 2 ones   =  30 + 2

+ 5 3     = 5 tens + 3 ones    =  50 + 3

8 5     = 8 tens + 5 ones    =  80 + 5

Method:

Step I: Add the ones,

2 ones + 3 ones = 5 ones.

Write 5 below the ones column.

Step II: Add the tens,

3 tens + 5 tens = 8 tens.

Write 8 below the tens column.

We can do the same problem in a short way. Steps remain the same as above.

T  O

3   2

+ 5   3

8   5

Therefore, 32 + 53 = 85

7. Let us now consider addition of 3 2-digit numbers 12, 14 and 53

 Step I: Write each digit of numbers in place value columns.Step II: (i) Add the ones and write in the once place.2 ones + 4 ones + 3 ones = 9 ones.
 (ii) Add the tens and write in the tens place. 1 ten + 1 ten + 5 tens = 7 tens.

Answer: 12 + 14 + 53 = 79

Regrouping

We can write a 2-digit number in different ways by regrouping it into tens and ones.

16 can be written as

8. Add 6 and 4.

Since we cannot have more than 9 beads in the ones rod, we change 10 ones to 1 ten and 0 ones.

Thus, 6 + 4 = 10

9. Add 58 and 34.

Step 1: Arrange the numbers in tens and ones.

 Step 2: Now, add the ones.8 ones + 4 ones = 12 onesSince 12 is more than 9,we change it to tens and ones.12 ones = 1 ten + 2 ones.Add. Carry over if needed.Write 2 in the ones place andcarry over 1 ten to the tens column.
 Step 3: Then, add the tens.5 tens + 3 tens = 8 tens 8 tens + 1 ten carried over = 9 tensWrite 9 in the tens place.Thus, 58 + 34 = 92

Addition of More than Two 2-Digit Numbers

Without Carrying

10. 16 + 32 + 21 = ?

 Step I: Arrange the numbers in tens and ones. Step II: Add the ones. Step III: Add the tens.

Thus, 16 + 32 + 21 = 69

Addition of Three Two Digit Numbers

11. Add 12, 31 and 22

T  O

1  2      =   1 ten + 2 ones   = 10  +  2

3  1      =   3 tens + 1 one   = 30  +  1

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

6  5      =   6 tens + 5 ones   = 60  +  5

Method:

Step I: Add the ones,

2 ones + 1 one + 2 ones = 5 ones.

Write 5 below the ones column.

Step II:

1 ten + 3 tens + 2 tens = 6 tens.

Write 6 below the tens column.

Therefore, 12 + 31 + 22 = 65

Addition of More than Two 2-Digit Numbers

With Carrying

12. 45 + 17 + 30 = ?

Step I: Arrange the numbers in tens and ones.

 Step II: Add the ones. Step III: Add the tens.

Thus, 45 + 17 + 30 = 92

Regrouping Tens

140 can be written as

 140 can be written as

or 1 hundred + 4 tens = 140

Sometime when we add two 2-digits numbers, we get a 3-digit number.

13. Add 60 and 40.

First put the ones beads together.

0     +     0      =     0

Then, put the tens beads together.

6 tens + 4 tens = 10 tens

Since we cannot have more than 9 beads in the tens rod,

we change 10 tens to 1 hundred.

Thus, 60 + 40 = 100

14. Add 85 and 42.

Step 1: Arrange the number in tens and ones

Step 2: Add the ones. 5 + 2 = 7

Step 3: Add the tens.

8 tens + 4 tens = 12 tens.

Regroup 12 tens into I hundred and 2 tens.

Write I in the hundreds place and 2 in the tens place.

Thus, 85 + 42 = 127

Addition With Carrying Twice

12. Add 69 and 55

Step 1: Arrange the numbers in tens and ones.

 Step 2: Add the ones Step 3: Add the tens. Step 4: Add the hundreds.

Thus, 69 + 55 = 124

Worksheet on Adding 2-Digit Numbers without Regrouping:

Addition of 2-Digit Numbers without Regrouping:

1. Find the sum of the two 2-Digit Numbers.

(i) 25 + 11

(ii) 14 + 32

(iii) 44 + 31

(iv) 53 + 22

(v) 16 + 12

(vi) 31 + 46

1. (i) 36

(ii) 46

(iii) 75

(iv) 75

(v) 28

(vi) 77

2. Find the sum of the three 2-Digit Numbers.

(i) 34 + 11 + 23

(ii) 45 + 22 + 31

(iii) 53 + 14 + 32

(iv) 11 + 22 + 33

(v) 71 + 14 + 13

(vi) 33 + 13 + 32

(vii) 23 + 45 + 11

(viii) 61 + 24 + 13

(ix) 54 + 13 + 22

(x) 44 + 11 + 10

2. (i) 68

(ii) 98

(iii) 99

(iv) 66

(v) 98

(vi) 78

(vii) 79

(viii) 98

(ix) 89

(x) 65

3. Addition of 2-Digit Numbers without Regrouping:

 (i) T     O              1     6         +   2     2         ________ (ii) T     O              2     3         +   3     1         ________
 (iii) T     O              4     6         +   1     1         ________ (iv) T     O              6     4         +   3     1         ________
 (v) T     O              7     1         +   2     6         ________ (vi) T     O              3     3         +   5     5         ________
 (vii) T     O              6     4         +   2     2         ________ (viii) T     O              5     7         +   3     2         ________
 (ix) T     O              2     1         +   1     6         ________ (x) T     O              1     6         +   5     3         ________

3. (i) 38

(ii) 54

(iii) 57

(iv) 95

(v) 97

(vi) 88

(vii) 86

(viii) 89

(ix) 37

(x) 69

4. Add the following 2-Digit Numbers with Carry Over if needed.

 (i) T     O              2     7         +   3     4         ________ (ii) T     O              1     4         +   1     8         ________
 (iii) T     O              3     8         +   3     5         ________ (iv) T     O              6     7         +   2     5         ________
 (v) T     O              2     2         +   2     9         ________ (vi) T     O              6     9         +   2     4         ________
 (vii) T     O              5     7         +   3     3         ________ (viii) T     O              2     1         +   1     9         ________
 (ix) T     O              5     6         +   3     8         ________ (x) T     O              4     4         +   2     4         ________

4. (i) 61

(ii) 32

(iii) 73

(iv) 92

(v) 51

(vi) 93

(vii) 90

(viii) 40

(ix) 94

(x) 68

5. Add the following more than two 2-Digit Numbers with Carry Over if needed.

 (i) T     O              2     1              4     0         +   2     2         ________ (ii) T     O              1     5              1     2         +   1     1         ________
 (iii) T     O              3     4              2     2         +   1     2         ________ (iv) T     O              4     2              3     3         +   1     2         ________
 (v) T     O              1     1              2     2         +   3     5         ________ (vi) T     O              2     1              2     5         +   1     0         ________
 (vii) T     O              3     0              2     8         +   1     0         ________ (viii) T     O              3     2              2     0         +   1     4         ________
 (ix) T     O              1     5              6     1         +   1     2         ________ (x) T     O              4     3              2     0         +   2     2         ________
 (xi) T     O              3     8              2     0         +   3     8         ________ (xii) T     O              3     2              1     8         +   2     9         ________
 (xiii) T     O              1     7              2     8         +   4     0         ________ (xiv) T     O              3     6              2     0         +   1     8         ________

5. (i) 83

(ii) 38

(iii) 68

(iv) 87

(v) 68

(vi) 56

(vii) 68

(viii) 66

(ix) 88

(x) 85

(xi) 96

(xii) 79

(xiii) 85

(xiv) 74

6. Add the following 2-Digit Numbers with Carrying Twice.

 (i) H       T       O                  4       0    +            6       1   ______________ (ii) H       T       O                  9       2    +            2       5   ______________
 (iii) H       T       O                  8       4    +            4       2   ______________ (iv) H       T       O                  6       3    +            7       6   ______________
 (v) H       T       O                  9       1    +            5       2   ______________ (vi) H       T       O                  2       5    +            8       2   ______________
 (vii) H       T       O                  7       6    +            5       1   ______________ (viii) H       T       O                  5       1    +            5       1   ______________
 (ix) H       T       O                  9       5    +            9       6   ______________ (x) H       T       O                  6       7    +            5       3   ______________
 (xi) H       T       O                  3       4    +            7       9   ______________ (xii) H       T       O                  4       8    +            8       5   ______________
 (xiii) H       T       O                  9       1    +            5       9   ______________ (xiv) H       T       O                  8       3    +            2       8   ______________
 (xv) H       T       O                  5       6    +            7       6   ______________ (xvi) H       T       O                  4       7    +            6       8   ______________

Word Problems on Adding 2-Digit Numbers:

7. (i) Rekha had 67 rupees. Her mother gave her 32 rupees more. How many rupees does Rekha have now?

(ii) In a zoo there were 46 monkeys and 33 deer. How many animals are there in the zoo?

(iii) Ramesh had 81 balloons. His brother Suresh gave him 17 balloons more. How many balloons does Ramesh have now?

(iv) Nairitee read 48 pages of her favourite book last week. She has 31 more pages to read until the end. How many pages does the book have?

7. (i) ₹ 99

(ii) 79

(iii) 98

(iv) 79

8. Paste number grid of 1 to 100 in your workbook and do the given activity.

 Take 2 by 2 grid, like:

Add diagonally (as indicated by arrows.)

You will get:

 4  4     +   5  5           9   9 5  4     +   4  5           9   9

What do you observe?

Oh! Yes, we get same answer 99.

Repeat this activity for some other 2 by 2 grid, say

What answer do you get? Is it same this time also?

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