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
Using an Abacus
For example:
1. Let us add 31 and 27 using an abacus.
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Step 1: Put the ones beads together. 1 + 7 = 8 |
Step 2: Put the tens beads together. 3 + 2 = 5 We 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 = 9 We 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.
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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
Addition without carrying:
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.
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.
6. Let us now consider addition of 3 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. |
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
Addition with Carrying
7. 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
8. Add 58 and 34.
Step 1: Arrange the numbers in tens and ones.
|
Step 2: Now, add the ones. 8 ones + 4 ones = 12 ones Since 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 and carry 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 tens Write 9 in the tens place. Thus, 58 + 34 = 92 |
Addition of More than Two 2-Digit Numbers
Without Carrying
9. 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 More than Two 2-Digit Numbers
With Carrying
10. 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
or 1 hundred + 4 tens = 140
Sometime when we add two 2-digits numbers, we get a 3-digit number.
11. 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
12. 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
Questions and Answers 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
Answer:
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
Answer:
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 ________ |
Answer:
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 ________ |
Answer:
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 ________ |
Answer:
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 ______________ |
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