Addition
Adding three 2-digit numbers involves the following steps:
1. Write the numbers vertically, aligning the digits by place value (tens and units).
2. Add the digits in the units place first.
– If the sum of the units digits is 10 or more, carry over the tens digit to the tens column.
3. Add the digits in the tens place, including any carry-over from the units place.
– Write down the result.
Example
Let’s add 34 + 27 + 58 .
1. Write the numbers vertically:
34
+27
+58 _______
`2. Add the digits in the units place (4 + 7 + 8):
– 4 + 7 = 11 (write down 1 and carry over 1 to the tens place)
– 11 + 8 = 19 (write down 9 and carry over 1 to the tens place)
34
+27
+58
_______
9 (1 carried over)
3. Add the digits in the tens place (3 + 2 + 5 + 1 carried over):
– 3 + 2 = 5
– 5 + 5 = 10
– 10 + 1 = 11
– Write down 11.
34
+27
+58
_______
119 So, 34 + 27 + 58 = 119 .
Breakdown
1. Units place:
– 4 + 7 = 11 → write 1, carry 1
– 11 + 8 = 19 → write 9, carry 1
– Result in the units place: 9
2. Tens place:
– 3 + 2 = 5
– 5 + 5 = 10
– 10 + 1 (carry) = 11
– Write 11
Therefore, the final result is 119.
The addition of larger 2-digit numbers
Example: Add 68 + 47
1. Write the numbers vertically, aligning the digits by place value (tens and units):
68
+47
_____
2. Start by adding the digits in the units place (8 + 7):
– 8 + 7 = 15
– Write down 5 in the units place and carry over 1 to the tens place.
68
+47
_______
5 (carry 1)
3. Next, add the digits in the tens place (6 + 4) along with the carry-over:
– 6 + 4 = 10
– Add the carried-over 1: 10 + 1 = 11
– Write down 11
68
+47
_______
115
So, 68 + 47 = 115 .
Step-by-Step Breakdown:
1. Write the numbers:
– Place 68 on top and 47 underneath, ensuring the digits are aligned by their place value.
2. Add the units place:
– 8 (units of 68) + 7 (units of 47) = 15
– Write 5 under the units column and carry over 1 to the tens column.
3. Add the tens place:
– 6 (tens of 68) + 4 (tens of 47) = 10
– Don’t forget the 1 you carried over: 10 + 1 = 11
– Write down 11 in the tens place.
Adding 3-digit number(without carrying)
Adding 3-digit numbers without carrying is a straightforward process because it means that when you add the digits in each column (ones, tens, hundreds), the sum is always less than 10. This ensures that there is no need to carry over any value to the next column.
Steps to Add 3-Digit Numbers Without Carrying:
1. Align the Numbers:
– Write the two 3-digit numbers one under the other, aligning their digits according to their place values (hundreds, tens, ones).
2. Add the Digits in the Ones Column:
– Start with the rightmost column (ones).
– Simply add the digits in this column.
3. Add the Digits in the Tens Column:
– Move to the middle column (tens).
– Add the digits in this column.
4. Add the Digits in the Hundreds Column:
– Finally, move to the leftmost column (hundreds).
– Add the digits in this column.
Since we are not carrying, the sum of the digits in each column will be less than 10, meaning the sum remains within that column without affecting the next column.
Example:
Let’s add 243 and 156 without carrying:
243
+ 156
——-
– Ones column: 3 + 6 = 9
– Tens column: 4 + 5 = 9
– Hundreds column: 2 + 1 = 3
So, the sum is:
243
+ 156
———
399
In this example, there’s no need to carry since all sums in each column are less than 10.
Adding 3-digit number(with carrying)
Adding 3-digit numbers with carrying involves a similar process to adding without carrying, but here, when the sum of digits in a column exceeds 9, you “carry” the extra value to the next column. This process ensures that the numbers are added correctly even when the digits add up to a number greater than 9.
Steps to Add 3-Digit Numbers with Carrying:
1. Align the Numbers:
– Write the two 3-digit numbers one under the other, aligning their digits according to their place values (hundreds, tens, ones).
2. Add the Digits in the Ones Column:
– Start with the rightmost column (ones).
– Add the digits in this column.
– If the sum is 10 or more, write down the rightmost digit of the sum in the ones place and carry over the leftmost digit to the tens column.
3. Add the Digits in the Tens Column:
– Move to the middle column (tens).
– Add the digits in this column along with any carried over value from the ones column.
– If the sum is 10 or more, write down the rightmost digit of the sum in the tens place and carry over the leftmost digit to the hundreds column.
4. Add the Digits in the Hundreds Column:
– Finally, move to the leftmost column (hundreds).
– Add the digits in this column along with any carried over value from the tens column.
– Write down the entire sum for this column since there are no more columns to carry over to.
Example:
Let’s add 487 and 356 with carrying:
487
+ 356
——–
– Ones column: 7 + 6 = 13
– Write down 3 in the ones place and carry over 1 to the tens column.
– Tens column: 8 + 5 = 13, then add the carried over 1: 13 + 1 = 14
– Write down 4 in the tens place and carry over 1 to the hundreds column.
– Hundreds column: 4 + 3 = 7 , then add the carried over 1: 7 + 1 = 8
– Write down 8 in the hundreds place.
So, the sum is:
487
+ 356
———
843
Key Points:
– Carrying happens when the sum of digits in any column is 10 or more.
– Carry Over the leftmost digit of the sum to the next column to the left.
– Write down only the rightmost digit of the sum in the current column.