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Checking Subtraction (I)

© Vidya Narayan Wadadekar

Teaching children how to check subtraction is very important. These checks are easy to handle and children can use them satisfactorily.

There are several methods for checking subtraction:

• As with addition, subtraction performed by one method can be checked by another method. This is shown in figure 1.

  In figure 1, the original subtraction is carried out by using the "Borrow Method." The same subtraction is then performed by using the "Carry Method." Since the answers obtained by both these methods match, the subtraction is correct.




• Another way of checking subtraction is adding the remainder to the subtrahend and confirming whether this sum is equal to the minuend. See this in figure 2(a).

  Here, after adding the subtrahend to the remainder of the subtraction, we get back a sum equal to the minuend; thus, the subtraction is correct.

  However, the subtraction 328 - 139 also could have been checked by following another subtraction, i.e., 328 - 189 (minuend - remainder of the subtraction). If we get back a sum equal to the subtrahend, the subtraction is correct. See this in figure 2(b).

• Casting out nines:
  We can check subtraction as shown in figure 3.
  
  

  To understand how it works read  "Speedy and accurate addition (Part III)" 

  However, as in the case of addition, it should be remembered that the calculation may be correct, but it is not necessarily so.

  To check subtraction by casting out nines, follow these steps:

  1. Calculate the remainder of nine for the minuend
  .
  2. Calculate the remainder of nine for the subtrahend
  .
  3. Calculate the remainder of nine for the remainder of the subtraction.
  4. Subtract the number obtained in Step 2 from Step 1. If the number obtained from this subtraction is equal to that obtained in step 3, then the subtraction is performed correctly. See examples 1 & 2 in Figure3.

     However, if the number obtained in Step 2 is greater than that obtained in Step 1, as shown in Example 3 in Figure3, you have to follow another subtraction,. Observe that we have subtracted the difference 2 again from 9 to get 7, as the actual remainder of 9.

  Can you guess why we subtracted 2 from 9?

  We will see the answer in the next article.

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