Addition
Method 1 - Partitioning
One method of adding numbers together is called "Partitioning". The number are broken down into parts, which recombine to find the total.
e.g. 53 + 16
53 + 16
Partitioning the numbers into tens and units: 50 + 3 + 10 + 6
Add the tens together: 50 + 10 = 60
Add the units together: 3 + 6 = 9
Recombine the numbers to give the total: 60 + 9 = 69
The knowledge of partitioning can also be used in vertical calculations, as shown below.
e.g. 53 + 16
5 3
1 6 +
Add the units together, ie 6 + 3: 9
Add the tens together, ie 50 + 10: 6 0 +
Total these numbers: 6 9
This method can also be applied to larger numbers.
e.g. 514 + 67
5 1 4
6 7 +
Add the units together, ie 4 + 7: 1 1
Add the tens together, ie 10 + 60: 7 0
Add the hundreds together, ie 500 + 0: 5 0 0 +
Total these numbers: 5 8 1
Method 2 - Regrouping/Carrying
In the third example above, adding the units together, ie 4 + 7, gives an answer of 11 which is made up of one ten and one unit:
T U
4
7 +
1 1
When using the regrouping method, the ten would be placed or "carried" into the tens column:
Step 1: Add the units together.
4 + 7 = 11
One ten is carried over and noted under the tens column and one unit is shown under the ones column:
5 1 4
6 7 +
1
1
Step 2: Add the tens together.
10 + 60 = 70
Add the one ten that has been carried over: 70 + 10 = 80
Eight tens are noted in the tens column:
5 1 4
6 7 +
1
8 1
Step 3: Add the hundreds together.
500 + 0 = 500
Five hundreds are noted in the hundreds column:
5 1 4
6 7 +
1
5 8 1
e.g. 397 + 426
Step 1: Add the units together.
7 + 6 = 13
One ten is carried over and noted under the tens column and three units are shown under the ones column:
3 9 7
4 2 6 +
1
3
Step 2: Add the tens together.
90 + 20 = 110
Add the one ten that has been carried over: 110 + 10 = 120
One hundred is carried over and noted in the hundreds column and two tens are noted in the tens column:
3 9 7
4 2 6 +
1 1
2 3
Step 3: Add the hundreds together.
300 + 400 = 700
Add the one hundred that has been carried over: 300 + 400 + 100 = 800
Eight hundreds are noted in the hundreds column.
3 9 7
4 2 6 +
1 1
8 2 3