Asked for the compound interest on £4,444 for 4,444

days at 4.5% per annum, Bidder, aged ten, gave the

answer, £2,434 16s 5.25d in two minutes.

When he was twelve he was asked "if a pendulum clock

vibrates the distance of 9.75 inches in a second of time,

how many inches will it vibrate in 7 years, 14 days, 2

hours, 1 minute, 56 seconds, each year being

365 days, 5 hours, 48 minutes, 55 seconds?"

He gave the answer, 2,165,625,744.75 inches,

*in less than 1 minute.*

George Parker Bidder (1806-1878) was the son of a stonemason
of

Devonshire, England. An elder brother taught him to count, this being

the only formal instruction in arithmetic he ever received. He

later became one of the most prominent civil engineers of his time.

2

CHAPTER 2

PRPORTIONATELY

Proportion is a natural and easy concept which is fundamental to mathematics.
It therefore offers some simple but very effective devices which we will be
using throughout subsequent chapters. With Proportion we will also be able
to extend considerably all the various formulas to come. The advantage of
splitting numbers into convenient sections is also illustrated in this chapter.

MULTIPLICATION BY 4, 8, 16, 20, 40 ETC.

Doubling numbers is very easy, so in multiplying a number, by say, 4 we simply
double the number twice.

Example 1
Example 2 |

Of course we can double more than twice. For multiplication by 8 we would double 3 times:

Example 3 |

And for multiplication by 16 we can double 4 times.

Example 4 |

In doubling 152 above you may find it easiest to double 15 to 30 and 2 to 4, and get 304, thereby thinking of the number in two convenient parts rather than three: 152 × 2 = 15/2 × 2 = 304. This number splitting is very effective and will be in frequent use.

Example 5 |

EXTENDING THE MULTIPLICATION TABLES

Example 6 |

MULTIPLICATION BY 5, 50, 25 ETC.

Halving numbers is also very easy, so rather than multiply by 5 we can put
a 0 onto the number and halve it, because 5 is half of 10.

Example 10 |

Since the halving of even numbers is to be preferred to the halving of odd numbers we may think of 2700 in this last example split as 2/70/0 so that 2 and 70 get halved to 1 and 35. In the example before that we think that half of 4/52/0 = 2/26/0.

For multiplication by 25 we multiply by 100 and halve twice, as 25 is half of half of 100.

Example 15 |

We may note here the use of the Vedic formula *Transpose and Apply*
in using division to do a multiplication sum. We can also transpose the devices
shown in this chapter to obtain easy methods of division by numbers like 4,
8, 25, 35 etc. For example to divide a number by 5 we double the number and
divide by 10:

Example 17 |

MULTIPLICATION
BY NUMBERS THAT END IN 5, 25, 75

Example 18 But 46 × 35 = 23 × 70 (by halving the first number and
doubling the Furthermore this has given us 23 to multiply instead of 46.
Example 19
Example 20 |

Multiplication by numbers ending in 25 or 75 can be given at least two applications
of this procedure:

Example 21 |

In these examples the first number has been even. But even if the first number
is odd it is still easier to multiply by twice the second number and then
halve the result.

Example 22
Example 23 |

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