Two-Digit Addition

Two-Digit Addition

Our assumption is that you know how to add and subtract one-digit numbers. We will begin with two-digit addition, something I suspect you can already do fairly well in your head. The following exercises are good practice, however, because the two-digit addition skills that you acquire here will be needed for larger addition problems, as well as virtually all multiplication problems in later lessons. This is the key to virtually every method you will learn in this blog. To paraphrase an old saying, there are three components to success—simplify, simplify, simplify.

The easiest two-digit addition problems are those that do not require you to carry any numbers, when the first digits sum to 9 or below and the last digits sum to 9 or below. For example:

                                         47

                   +32(30+2)

To solve 47 +32, first add 30, then add 2. After adding 30, you have the simpler problem 77 +2, which equals 79. We illustrate this as follows:

  47 +32      =     77 +2    =     79

                        (first add 30)                   (then add 2)

The above diagram is simply a way of representing the mental processes involved in arriving at an answer using our method. While you need to be able to read and understand such diagrams as you work your way through this book, our method does not require you to write down anything yourself.

Now let’s try a calculation that requires you to carry a number:

                                                   28

                         +36(30+6)

Adding from left to right, you can simplify the problem by Adding 28+30=58; then 58+6=64.

   28 +36      =     58 +6    =     64

                           (first add 30)                   (then add 2)

Was that easier? If you would like to try your hand at more two-digit addition problems, check out the set of exercises below.

1.     44 + 67 =

2.     56 + 87 =

3.     76 + 43 =

4.     98 + 32  =

5.     78 + 83 =

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Three-Digit Addition

Three-Digit Addition

The strategy for adding three-digit numbers is the same as for adding two-digit numbers: you add from left to right. After each step, you arrive at a new (and simpler) addition problem. Let’s try the following:

                                                473

                        +326(300+20+6)

Starting with 473, we add 300, then add 20, then add 6. After adding 300 (473 +300=773), the problem becomes 773+26. After adding 20 (773+20=793), the problem simplifies to 793+6=799. This thought process can be diagrammed as follows:

473  +  326  =  773  +  26   =  793  +  6  =  799

                      +300                        +20                   +6

Let’s try another one for practice:

                                                   568

                         +496(400+40+6)

Then,

568  +  496  =  968  +  96   =  1058  +  6  =  1064

                        +400                      +90                   +6

This addition problem is a little more difficult than the last one since it requires you to carry numbers in all three steps. However, with this particular problem you have the option of using an alternative method. I am sure you will agree that it is a lot easier to add 500 to 759 than it is to add 496, so try adding 500 and then subtracting the difference:

                                                  568

                        +496(500-6)

Then

568  +  496  =  1068  -  4  =  1064

                       ( First add  +500)          ( then subtract  -6  )                               

Practice the following three-digit addition exercises,

1.      345 + 451  =

       2.   673 + 496 =

.      3.   786 + 429 =

    4.    369 + 345 =

    5.    281 + 496 =

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