Adding Two-Digit Numbers Using Money

Date: 09/13/2001 at 18:40:56
From: Vicki 
Subject: Adding 2-digit numbers

Dear Dr. Math, 

I don't understand how to add 2-digit numbers like 24 + 56 + ? Can you 
please help?

Vicki

Date: 09/13/2001 at 23:14:17
From: Doctor Peterson
Subject: Re: Adding 2-digit numbers

Hi, Vicki.

I like to get out some money (play money if you prefer) to talk about 
this. Get some, and then follow along.

First, lay down 24 dollars, by putting 2 ten-dollar bills in one pile, 
and 4 one-dollar bills in another:

     _  _    _  _         _ _    _ _    _ _    _ _
    |_10_|  |_10_|       |_1_|  |_1_|  |_1_|  |_1_|

Now add to that 56 dollars, in the form of 5 more tens and 6 more 
ones:
     _  _    _  _         _ _    _ _    _ _    _ _
    |_10_|  |_10_|       |_1_|  |_1_|  |_1_|  |_1_|

          +                          +
     _  _    _  _         _ _    _ _    _ _    _ _
    |_10_|  |_10_|       |_1_|  |_1_|  |_1_|  |_1_|
     _  _    _  _         _ _    _ _
    |_10_|  |_10_|       |_1_|  |_1_|
     _  _
    |_10_|

Now how much do you have? We have 2 + 5 = 7 ten-dollar bills, and 
4 + 6 = 10 one-dollar bills. If there were fewer than 10 ones, we 
would have been able to write down the answer immediately. But in this 
case that would make it "seventy-ten," which isn't quite how we say 
numbers! So we go to the banker and ask for a ten-dollar bill in place 
of our ten one-dollar bills:
     _  _    _  _
    |_10_|  |_10_|               (no ones)
     _  _    _  _
    |_10_|  |_10_|
     _  _    _  _
    |_10_|  |_10_|
     _  _    _  _
    |_10_|  |_10_|

Now instead of 7 tens and 10 ones, we have 8 tens, which is 80 
dollars. So 

   24 + 56 = 80.

How can you do that without money? You write it down this way:

      24
    + 56
    ----

The numbers just stand for our piles of bills. We add the 4 and 6 ones 
and get 10; since that is too big for one digit, we make change 
("carry" or "regroup") and think of it as 1 ten and no ones. So we 
write down the number of ones (0), and put an extra 1 in the tens pile 
(I mean, column):

      1
      24
    + 56
    ----
       0

Now we add all our tens: 1+2+5 = 8. Write that down and we have our 
number:

      1
      24
    + 56
    ----
      80

Try doing the same thing with every problem you have to do, until you 
get tired of it and realize you don't need the money but can just 
write down the answer.

If you need any more help with this, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/