Home      Site Map

Column Multiplication: Carrying

Sometimes, you will see an equation that will require carrying. Here's an example that demonstrates carrying:

   
 
 
 
  
 
 
 
5
6
×
 
 
8
3

   
 
 
  
   
 
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
   White Box   White Box   White Box   White Box

Right To Left. We first see the 6, which is above the 3.  6 × 3 = 18. Because 18 is greater than 9, we put the 8 in the box below the 3. Then, we put the 1 in the box above the 5: this is carrying. Our equation is now:

   
 
 
 
  
 
 
 
5
6
×
 
 
8
3

   
 
 
  
   
 
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
   White Box   White Box   White Box   White Box

5 × 3 = 15.  Then, we add the 1 that we just carried to 15.  15 + 1 = 16.   Our equation is now:

   
 
 
 
  
 
 
 
5
6
×
 
 
8
3

   
 
 
  
   
 
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
   White Box   White Box   White Box   White Box

We are finished with the 3 in the second row. So, going from Right To Left we see the 8. But before we start again from Right to Left in the top row, we must put a 0 in the rightmost box in the next row where we are writing the results:

   
 
 
 
  
 
 
 
5
6
×
 
 
8
3

   
 
 
  
    
  
    
  
    
  
    
  
   
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
   White Box   White Box   White Box   White Box

Going from Right to Left in the first row, 6 × 8 = 48.  Because 48 is greater than 9, we put the 8 in the box next to the 0. Then, we put the 4 in the box above the 5: this is carrying. We just get rid of the 1 that was there because we no longer need it. Our equation is now:

   
 
 
 
  
 
 
 
5
6
×
 
 
8
3

   
 
 
  
    
  
    
  
    
  
    
  
   
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
   White Box   White Box   White Box   White Box

Going from Right to Left in the first row, 5 × 8 = 40.  Then, we add the 4 that we just carried to 40.   4 + 40 = 44  Because 5 is the leftmost number in the first row, we just put 44 in the boxes next to where we first wrote a 0 and then an 8. Our equation is now:

   
 
 
 
  
 
 
 
5
6
×
 
 
8
3

   
 
 
  
    
  
    
  
    
  
    
  
   
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
   White Box   White Box   White Box   White Box

We're almost finished. Now, we use what we learned about column addition to add 168 plus 4480:

   
 
 
 
  
 
 
 
5
6
×
 
 
8
3

   
 
 
  
    
  
    
  
    
  
    
  
   
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
   White Box   White Box   White Box   White Box

Because of column addition, we put a 1 in the leftmost box in the first row. The answer is 4648.
We didn't write a plus sign when we added because most people don't: they know that they have to do addition.

The following example uses three columns:

   
 
 
 
 
  
 
  
 
 
 
 
2
6
8
×
 
 
 
9
7
4

   
 
 
  
 
  
 
  
   
 
 
 
  
 
  
 
  
 
  
   
 
 
  
 
  
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  
 
  
 
  

   
 
 
  
 
  
 
  
 
  
 
  

Right to Left. We go from right to left in the top row. We start by multiplying each number in the top row by the rightmost number in the second row. 8 × 4 = 32. Because 32 is greater than 9, we put the 2 in the box below the 4 in 974. Then, we put the 3 in the box above the 6 in 268: this is carrying. Our equation is now:

   
 
 
 
 
  
 
  
 
 
 
 
2
6
8
×
 
 
 
9
7
4

   
 
 
  
 
  
 
  
   
 
 
 
  
 
  
 
  
 
  
   
 
 
  
 
  
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
 
  
 
  

We continue to go from right to left in the top row.  6 × 4 = 24. We have to add 3 + 24 because of the 3 we just carried. 3 + 24 = 27. Because 27 is greater than 9, we put the 7 in the box below the 7 in 974. Then, we put the 2 in the box above the 2 in 268: this is carrying. Our equation is now:

   
 
 
 
 
  
 
  
 
 
 
 
2
6
8
×
 
 
 
9
7
4

   
 
 
  
 
  
 
  
   
 
 
 
  
 
  
 
  
 
  
   
 
 
  
 
  
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
 
  
 
  

We continue to go from right to left in the top row. 2 × 4 = 8. We have to add 2 + 8 because of the 2 we just carried. 2 + 8 = 10. We put the 1 and the 0 in the two textboxes that are next to the 7 and the 2. Our equation is now:

   
 
 
 
 
  
 
  
 
 
 
 
2
6
8
×
 
 
 
9
7
4

   
 
 
  
 
  
 
  
   
 
 
 
  
 
  
 
  
 
  
   
 
 
  
 
  
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
 
  
 
  

We are finished with the 4 in the second row. So, going from Right To Left in the second row we see the 7. But before we start again from Right to Left in the top row, we must put a 0 in the rightmost box in the next row where we put the results. We do this because the 7 is one number away from the 4:

   
 
 
 
 
  
 
  
 
 
 
 
2
6
8
×
 
 
 
9
7
4

   
 
 
  
 
  
 
  
   
 
 
 
  
 
  
 
  
 
  
   
 
 
  
 
  
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
 
  
 
  

Right to Left. We go from right to left in the top row. We multilply each number in the top row by the 7 in the second row. 8 × 7 = 56. Because 56 is greater than 9, we put the 6 in the box next to the 0 that we just wrote. Then, we put the 5 in the box above the 6: this is carrying. We just get rid of the 3 that was there because we no longer need it. Our equation is now:

   
 
 
 
 
  
 
  
 
 
 
 
2
6
8
×
 
 
 
9
7
4

   
 
 
  
 
  
 
  
   
 
 
 
  
 
  
 
  
 
  
   
 
 
  
 
  
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
 
  
 
  

We continue to go from right to left in the top row.  6 × 7 = 42. We have to add 5 + 42 because of the 5 we just carried. Because 47 is greater than 9, we put the 7 in the box next to the 6 that we just wrote. Then, we put the 4 in the box above the 2 in 268: this is carrying. We just get rid of the 2 that was there because we no longer need it. Our equation is now:

   
 
 
 
 
  
 
  
 
 
 
 
2
6
8
×
 
 
 
9
7
4

   
 
 
  
 
  
 
  
   
 
 
 
  
 
  
 
  
 
  
   
 
 
  
 
  
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
 
  
 
  

The leftmost number in the top row is 2.  2 × 7 = 14. We have to add 4 + 18 because of the 4 we just carried: 4 + 18 = 22.  Because 2 is the leftmost number in the top row, we just put a 1 and an 8 in the boxes next to where we just put 7, 6, and 0. Our equation is now:

   
 
 
 
 
  
 
  
 
 
 
 
2
6
8
×
 
 
 
9
7
4

   
 
 
  
 
  
 
  
   
 
 
 
  
 
  
 
  
 
  
   
 
 
  
 
  
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
 
  
 
  

We are finished with the 7 in the second row. So, going from Right To Left in the second row we see the 9. But before we start again from Right to Left in the first row, we must put a 0 in the two rightmost boxes in the next row where we put the results. We do this because the 9 is two numbers away from the 4:

   
 
 
 
 
  
 
  
 
 
 
 
2
6
8
×
 
 
 
9
7
4

   
 
 
 
  
 
  
 
  
   
 
 
 
  
 
  
 
  
 
  
   
 
 
  
 
  
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
 
  
 
  

Right to Left. We go from right to left in the top row. We multilply each number in the top row by the 9 in the second row. 8 × 9 = 72. Because 8 × 9 is greater than 9, we put the 2 in the box next to the two zeros. Then, we put the 7 in the box above the 6: this is carrying. We just get rid of the 5 that was there because we no longer need it. Our equation is now:

   
 
 
 
 
  
 
  
 
 
 
 
2
6
8
×
 
 
 
9
7
4

   
 
 
  
 
  
 
  
   
 
 
 
  
 
  
 
  
 
  
   
 
 
  
 
  
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
 
  
 
  

We continue to go from right to left in the top row.  6 × 9 = 54. We have to add 7 + 54 because of the 7 we just carried. Because 61 is greater than 9, we put the 1 in the box next to the 2 that we just entered. Then, we put the 6 in the box above the 2 in 268: this is carrying. We just get rid of the 4 that was there because we no longer need it. Our equation is now:

   
 
 
 
 
  
 
  
 
 
 
 
2
6
8
×
 
 
 
9
7
4

   
 
 
  
 
  
 
  
   
 
 
 
  
 
  
 
  
 
  
   
 
 
  
 
  
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
 
  
 
  

The leftmost number in the top row is 2.  2 × 9 = 18. We have to add 4 + 18 because of the 4 we just carried. Because 2 is the leftmost number in the top row, we just put a 1 and an 8 in the boxes next to where we just put 7, 6, and 0. Our equation is now:

   
 
 
 
 
  
 
  
 
 
 
 
2
6
8
×
 
 
 
9
7
4

   
 
 
  
 
  
 
  
   
 
 
 
  
 
  
 
  
 
  
   
 
 
  
 
  
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
 
  
 
  

We're almost finished. Now, we must use what we learned in Column Addition to add 1072 plus 18760 plus 241200:

   
 
 
 
 
  
 
  
 
 
 
 
2
6
8
×
 
 
 
9
7
4

   
 
 
  
 
  
 
  
   
 
 
 
  
 
  
 
  
 
  
   
 
 
  
 
  
 
  
 
  
 
  
   
 
  
 
  
 
  
 
  
 
  
 
  

   
 
  
 
  
 
  
 
  
 
  
 
  

The answer is 261032.

Continue to Next Page