CLASS-1
ADDITION WITH REGROUPING
ADDITION WITH REGROUPING -
Addition with regrouping, also known as carrying, is used when the sum of digits in a column is greater than 9. Let's go through an example of adding two three-digit numbers:
Example.1) 4 2 6
+ 3 5 9
__________
Step 1: Start by adding the rightmost digits, which are 6 and 9.
4 2 6
+ 3 5 9
__________
1 5
Step 2: Write down the result (15) below the line.
Step 3: Move to the next column (the tens place) and add the digits, including the carry from the previous step. In this case, it's 2 + 5 + 1 (the carry from Step 1).
4 2 6
+ 3 5 9
_________
1 5
1 7
Step 4: Write down the result (17) below the line.
Step 5: Move to the next column (the hundreds place) and add the digits, including the carry from the previous step. In this case, it's 4 + 3 + 1 (the carry from Step 3).
4 2 6
+ 3 5 9
_________
1 5
1 7
7
Step 6: Write down the result (7) below the line.
Step 7: The final result is obtained by combining all the digits written below the line. So, the sum of 426 and 359 is 785.
Therefore, 426 + 359 = 785.
In this example, regrouping (carrying) was required in two columns, as the sums exceeded 9.
Example.2)
2 7
+ 5 9
__________
Step 1: Start by adding the rightmost digits, which are 7 and 9. The sum is 16.
2 7
+ 5 9
_________
6
Step 2: Since the sum in this column is 16, which is greater than 9, we need to regroup or carry over. Write down the units digit (6) and carry over the tens digit (1) to the next column.
2 7
+ 5 9
_________
1 6
Step 3: Move to the next column and add the digits, considering the carried-over tens digit. In this case, we have 1 (carried-over) + 2 + 5, resulting in 8.
2 7
+ 5 9
_________
8 6
Step 4: Since there are no more columns to add, we have our final sum, which is 86.
So, in this example, addition with regrouping was required because the sum of the rightmost digits exceeded 9. The tens digit was carried over to the next column to obtain the correct result.
For more clarification, we need to discuss with more examples -
1) Add 56 + 38 = ?
METHOD OF SOLUTION
Step 1.- Add the ‘Ones’.
6 Ones + 8 Ones = 14 Ones
14 Ones = 1 Tens 4 Ones
Write 4 in the ‘ Ones’ column and take 1 Tens to the ‘Tens’ column.
Step 2. - Add the ‘ Tens’.
1 Tens + 5 Tens + 3 Tens = 9 Tens.
Write 9 Tens to the ‘ Tens’ Column.
So, the answer is 94. (Ans.)
2) Add 39 + 29 = ?
METHOD OF SOLUTION
Step 1.- Add the ‘Ones’.
9 Ones + 9 Ones = 18 Ones
18 Ones = 1 Tens 8 Ones
Write 8 in the ‘ Ones’ column and take 1 Tens to the ‘Tens’ column.
Step 2. - Add the ‘ Tens’
1 Tens + 3 Tens + 2 Tens = 6 Tens.
Write 6 Tens to the ‘ Tens’ Column.
So, the answer is 68 . (Ans.)
3) Add 57 + 36 = ?
METHOD OF SOLUTION
Step 1.- Add the ‘Ones’.
7 Ones + 6 Ones = 13 Ones
13 Ones = 1 Tens 3 Ones
Write 3 in the ‘ Ones’ column and take 1 Tens to the ‘Tens’ column.
Step 2. - Add the ‘Tens’
1 Tens + 5 Tens + 3 Tens = 9 Tens.
Write 9 Tens to the ‘ Tens’ Column.
So, the answer is 93 . (Ans.)
4) Add 27 + 28 + 36 = ?
METHOD OF SOLUTION
Step 1.- Add the ‘Ones’.
7 Ones + 8 Ones + 6 Ones = 21 Ones
21 Ones = 2 Tens 1 Ones
Write 1 in the ‘ Ones’ column and take 2 Tens to the ‘Tens’ column.
Step 2. - Add the ‘Tens’
2 Tens + 2 Tens + 2 Tens + 3 Tens= 9 Tens.
Write 9 Tens to the ‘ Tens’ Column.
So, the answer is 91 . (Ans.)
5) Add 18 + 37 + 29 = ?
METHOD OF SOLUTION
Step 1.- Add the ‘Ones’.
8 Ones + 7 Ones + 9 Ones = 24 Ones
24 Ones = 2 Tens 4 Ones
Write 4 in the ‘ Ones’ column and take 2 Tens to the ‘Tens’ column.
Step 2. - Add the ‘Tens’
2 Tens + 1 Tens + 3 Tens + 2 Tens= 8 Tens.
Write 8 Tens to the ‘ Tens’ Column
So, the answer is 84. (Ans.)
6) Add 37 + 32 + 19 = ?
METHOD OF SOLUTION
Step 1.- Add the ‘Ones’.
7 Ones + 2 Ones + 9 Ones = 18 Ones
18 Ones = 1 Tens 8 Ones
Write 8 in the ‘ Ones’ column and take 1 Tens to the ‘Tens’ column.
Step 2. - Add the ‘Tens’
1 Tens + 3 Tens + 3 Tens + 1 Tens = 8 Tens.
Write 8 Tens to the ‘ Tens’ Column.
So, the answer is 88. (Ans.)