ON A TRAIN

NOT-SO-LONG DIVISION

On a long train journey?- liven up your trip with this marvellous method for dividing numbers.

As in the case of ‘long’ multiplication ‘long’ division in this system is not long at all and, in fact, the answer to any division sum can be put down in one line.

**369 ÷ 72 = 5 remainder 9**

We use**THE FIRST BY THE FIRST AND THE LAST BY THE LAST**.

Divide the 36 at the beginning of 369 by the first figure of 72: 36 ÷ 7 = 5 remainder 1.

This gives: 36_{1}9 ÷ 72 = 5

The remainder, 1, is placed as shown and makes 19 with the 9 following it.

From this 19 we subtract 2 × 5 (the answer figure multiplied by last figure of 72):

19 - 10 = 9, the remainder.

To sum up: for**369 ÷ 72**:

36 ÷ 7 = 5 remainder 1 gives**36**_{1}9 ÷ 72 = 5

and 19 - 2 × 5 = 9 the remainder,

so**36**_{1}9 ÷ 72 = 5 rem 9

- Similarly
**468 ÷ 73 = 6 remainder 30**

Because 46 ÷ 7 = 6 remainder 4: 46_{4}8 ÷ 73 = 6,

then 48 - 3 × 6 = 30, the remainder.

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On The Train

Similarly squares, squares roots are easily tackled (in one line) by the Vedic method. We can also solve equations and geometrical and trigonometrical problems. The Vedic system covers all areas of mathematics.

It is not possible to show all variations of the methods in this book: all the techniques shown can be extended in various ways.