The ‘Why’ of division algorithm

Monica Kochar

How many times have you taught a division problem this way?

Divide 245 by 7
245-by-7 Here 245 is the dividend and 7 is the divisor
Since the 1st digit of the dividend, 2, is less than the divisor, 7
I am going to take the 2nd digit also to get 24. 24 is more than 7 and hence I can divide!
7 multiplied by 3 is 21 and hence I divide 24 by 7 to get 3 in the quotient and 3 as remainder.
Now I open the next digit.
And I bring down 5 to get 35.
35 is bigger than 7 and hence I can divide it. 35 in fact is divisible by 7 completely.
7 times 5 is 35 and hence remainder is 0. End of division.
Quotient 35 and Remainder 0.

But why?
Did you ever wonder why? Why do we hide the digit to check the 1st digit and if it is smaller than the divisor then check the next digit and so on?

Because our teacher taught us so?

But it is high time we ask ‘why?’ Or else we will murder maths in the young minds. Algorithm without logic is murder.

The author has taught math for 19 years in Indian and international schools. She also works as a curriculum developer and mentor for math curriculum. She can be contacted at She also has a facebook page

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