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Checking division

© Vidya Narayan Wadadekar

Children feel more confident in solving division problems, if they are able to check accuracy of their work themselves. Therefore, as soon as they understand what division is and how it can be accomplished, we should teach them the different methods of checking division. Usually children themselves find out ways of checking division computations.

One way of checking the division work for possibility of inaccuracy is performing the corresponding inverse operation. In other words division can be checked by performing multiplication. This is shown below using simple division.

Let us take a more complex division and see how it can be checked using multiplication.

Note that in the example ‘divide 38985 by 165’ there is a remainder (which is 45) after division. Hence, after multiplying the divisor and the quotient we must add the reminder to the product. The sum results into the dividend. This shows that we have accomplished the division correctly!

Another way of checking division is by performing division operation suggested by the commutative law. According to the commutative law if we divide the dividend by the quotient we would get back the divisor. This information we can use to check accuracy of division. This is illustrated below using the division problems solved above.

In the first example, 7 was the divisor and the quotient obtained was 8. However, when we used 8 as the divisor, 7 took the position of the quotient. Whereas in the second example, when the divisor was 165, the quotient obtained was 236. However, when we used 236 as the divisor, the quotient obtained was 165. Note that in the case of both divisions remainder remained the same i.e. zero in the first example and 45 in the second example.

The two ways of checking division discussed so far are quite inconvenient to apply. Number of steps involved in these checks is comparable to those involved in solving the original problem. Thus the checks themselves are likely to contain errors. We therefore need a check that is very easy to apply and has lesser number of steps reducing chances of errors.

One such simple check is by casting out nines. Logic involved in casting out nines is discussed in detail in the articles Speedy and accurate addition (Part III) and Checking multiplication.

To check division by casting out nines, replace the divisor, dividend, quotient, and remainder by the results after casting out nines. If all the replaced numbers hold the relationships exactly similar to that held by the original numbers, then the division is correct. This is shown below with the help of the division problems used earlier.