Addition Regrouping

Addition
Of Two-Digit Numbers With Regrouping

An example of addition of two-digit number with regrouping is 27+46. There are many methods to solve such problems. You can chose whichever is most comfortable for you, or even invent your own. The most important thing is for the answer to be correct. Here we will discuss three different methods for the mental calculation of these problems.

Method 1: This method has three steps.
1. First you add the numbers in the tens place. Using the above example…
2 tens + 4 tens = 6 tens
20 + 40 = 60
2. Now add the ones…
7 ones + 6 ones = 13 ones
7 + 6 = 13
3: Now combine:
60 + 13 = 73
So 27 + 46 = 73.
Try these practice problems using Method 1;
Practice 1:
____18 + 23____
Add tens
10 + 20 = ____(30)_____
Add ones
8 + 3 = ___(11)_____
Combine
__(30)___ + __(11)___ = ___(41)_____

Practice 2:
_____25 + 68_____
20 + 60 = (90)
5 + 8 = (13)
(80) + (13) = (93)

Practice 3:
_____32 + 49_____
30 + (40) = (70)
2 + (9) = (11)
(70) + (11) = (81)

Practice 4:
_____74 + 17_____
(70) + 10 = (80)
(4) + 7 = (11)
(80) + (11) = (91)

Solve Mentally (without using paper)
1.  78 + 16
2.  35 + 26
3.  27 + 67
4.  19 + 29
5.  55 + 37
6.  44 + 49

Method 2: This method has three steps.
Reminder: The two numbers being added together are called ADDENDS. The answer is called the SUM.
1. Split one of the addends into the tens digit plus the ones digit.
46 = 4 tens + 6 ones
46 = 40 + 6
2. Add the tens to the other addend.
27 + 40 = 67
3. Now add the ones to get the final sum.
67 + 6 = 73

Try these practice problems using Method 2;
Practice 1:
____19 + 34____
Split the second addend: 30 + 4 = ___(34)_____
Add tens to first addend: 19 + 30 = ___(49)____
Add ones to get final sum: __(49)___ + __(4)___ = ___(53)_____

Practice 2:
____57 + 36____
Split the first addend: 50 + 7 = _____(57)_____
Add tens to second addend: 0 + 36 = ___(86)____
Add ones to get final sum: ___(86)___ + ___(7)___ = ____(93)_____

Practice 3:
_____47 + 34_____
34 = (30) + (4)
47 + (30) = (77)
(77) + (4) = (81)

Practice 4:
_____28 + 25_____
28 = (20) + (8)
28 + (20) = (48)
(48) + (5) = (53)

Solve mentally (without using paper)
1. 35 + 17
2. 42 + 39
3. 54 + 28
4. 19 + 14
5. 63 + 29
6. 75 + 16

Method 3: This method has three steps
Reminder: Rounding to the nearest ten is taking a number and making it the nearest round number, or multiple of ten [10, 20, 30, 40, etc]. When the ones digit is from 0 to 4, the tens digit stays and the ones digit becomes 0. When the ones digit is from 5 to 9, the tens digit increases by 1 and the ones digit also becomes 0. [44 rounded = 40, 45 rounded =50]
1. Round the first addend.
27 à30
2. Add the second addend to the rounded number.
30 + 46 = 76
3. Adjust. However much higher or lower you rounded, subtract or add the same amount, respectively. If you added to get a round number, subtract that amount to adjust. If you rounded down, add that amount.
76 - 3 = 73
*The 3 is from the adjustment of 27 to 30*

Try these practice problems using Method 3;
Practice 1:
____38 + 16____
Round the second addend: 6 à ____(20)____
Add round number to first addend: 38 + 20 = ____(58)____
Adjust to get final sum: ___(58)___ - ___(4)___= ____(54)_____

Practice 2:
____39 + 55____
Round the first addend: 39 à___(40)_____
40 + 55 = ____(95)____
___(95)___ - ___(1)___ = ___(94)_____

Practice 3: _____72 + 19_____
72 à(70)
(70) + (19) = (89)
(89) + (2) = (91)

Practice 4:
_____58 + 23_____
23à(20)
(58) + (20) = (78)
(78) + (3) = (81)
Solve mentally (without using paper)
1. 66 + 27
2. 34 + 19
3. 16 + 45
4. 43 + 48
5. 59 + 17
6. 62 + 19