Quick division by two

Dividing any number by two using paper-pencil is a very easy job. However, you would be surprised to know that dividing any number by two instantly without using paper-pencil is also very easy. In fact you can give the answer as soon as a person completes saying the number he wants you to divide by two!

For this we need to use our experience of dividing all the single digit numbers by two. What happens when we divide numbers from 1 to 9 by two? The quotients and remainders we have with each of these divisions are consolidated in the following table:

Thus, the only remainder we have to account for while dividing any number by two is "one". This fact makes division by 2 very easy!

We now study effect of the remainder "one" on the process of division by two. To do this let us divide 54 by two.

The first digit of the number 54 is 5, from where we begin division. Dividing 5 by two, we get quotient 2 and remainder 1. This remainder is actually one tens, hence can give 10 units. As you know 10 units are completely divisible by 2 giving 5 units. Therefore, we add these 5 to the quotient obtained by dividing the remaining 4 units of the number 54 by two. When we divide four by two, we get 2 as the quotient, which we add to the 5, obtained from the remainder of the earlier division (5 divided by 2). Thus, we get 7 in the units place of the quotient.

We can do it orally by saying: 5 divided by two equals 2, remainder 1. 5 plus "4 divided by two" equals 7 (no remainder). Thus, 54 divided by two equals 27. Check out the answer. Two times 27 equals 54. The division is correct!

Lets us take another example, 135 divided by 2.

Can we do it orally? Yes, we do it by saying: 1 divided by two equals 0, remainder 1. 5 plus "3 divided by two" equals 6, remainder 1. 5 plus "5 divided by two" equals 7 and remainder 1. Thus, 135 divided by 2 equals 67 and remainder 1. Check out the answer. Two times 67 equals 134, plus 1 equals 135. The division is correct!

How we have managed the division by two? We have simply divided each single digit starting from the left by two. However, if we encountered a remainder 1, we have added 5 in the quotient of the division of the next digit! And when we do not have next digit to be divide by two, we simply mention 1 as the remainder of the complete division.

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