Arithmetic Grade Five

Lesson Three: Addition Review

Carrying (or regrouping) can be difficult at first since most students like to just fall back on counting up the sum. Counting up the sum works, but it can be very slow compared to carrying. Here's another example for you to study. 

   37
  +43
  ----
When we add up the digits in the ones column we get 10 and so we write the one above the tens column and the 0 in the ones column in the answer space: 

   1
   37
  +43
  ----
    0
Next we add up all the numbers in the tens column: 

   1
   37
  +43
  ----
   80
Here's another example: 

    47
   +49
   ----
Problem without answer

    1
    47
   +49
   ----
     6
Adding the 7 and 9 in the ones column we get 16. We take the 6 from 16 and place it in the ones column of the answer and we carry the 1 above the tens column above the addends.

    1
    47
   +49
   ----
    96
We add up the 1, 4, and 4 in the tens column.


Alternative Algorithm: For those of you who like different ways of doing problems here's a slightly altered method to solve these problems: 

    28
   +29
  -----
Original Problem 

    28
   +29
  -----
    17
Partial sum for the ones: 8 + 9 = 17 

    28
   +29
  -----
    17
    40
Partial sum for the tens: 20 + 20 = 40 

    28
   +29
  -----
    17
    40
  -----
    57
Add Up Partial Sums: 17 + 40 = 57
As you can see this method will work to calculate the sum of an addition problems. The steps are just a little different. This is not the standard method used to solve these problems, but it works!

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