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Column Addition: Carrying and Regrouping

Sometimes, you will see an equation that you can't solve just by using simple addition. Here's an example:

    
  
 
3
5
+
2
7
   
 
  
 
  
   White Box   White Box

Right To Left. We first see the 5, which is above the 7.  5 + 7 = 12. We put the 2 (from the 12) below the 7 and the 1 (from the 12) above the next column to the left.

Our equation is now:

    
  
   White Box
 
3
5
+
2
7
   
 
  
 
  
   White Box   White Box

Again we go from Right To Left and see the 1 above the 3.  1 + 3 = 4 and 4 + 2 = 6. Our equation is now:

    
  
 
3
5
+
2
7
   
 
  
 
  
   White Box   White Box

So, the answer is 62.

Here's another example:

    
  
    
  
    
  
    
  
 
 
8
4
5
+
 
3
2
9
   
 
  
 
  
 
  
 
  
   White Box   White Box   White Box   White Box

Right To Left. We first see the 5, which is above the 9.  5 + 9 = 14. We put the 4 (from the 14) below the 9 and the 1 (from the 14) above the next column to the left.

Our equation is now:

    
  
    
  
    
  
    
  
 
 
8
4
5
+
 
3
2
9
   
 
  
 
  
 
  
 
  
   White Box   White Box   White Box   White Box

Again we go from Right To Left and see the 1 above the 4.  1 + 4 = 5 and 5 + 2 = 7. Our equation is now:

    
  
    
  
    
  
    
  
 
 
8
4
5
+
 
3
2
9
   
 
  
 
  
 
  
 
  
   White Box   White Box   White Box   White Box

Once again we go from left to right. 8 + 3 = 11. Because there are no more columns, we just write the 11 below the 3:

    
  
    
  
    
  
    
  
 
 
8
4
5
+
 
3
2
9
   
 
  
 
  
 
  
 
  
   White Box   White Box   White Box   White Box

So, the answer is 1174.

The process of putting a 1 above the equation when needed is called carrying or regrouping.

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