To multiply by 2 is the same as to multiply by 10 and divide by 5.

Any number of figures you may wish to multiply by 5, will give the same result if divided by 2 - a much quicker operation than the former; but you must remember to annex a cipher to the answer where there is no remainder, and where there is a remainder, annex a 5 to the answer. Thus, multiply 464 by 5, the answer will be 2320; divide the same number by 2, and you have 232, and as there is no remainder, you add a cipher. Now, take 357, and multiply by 5 - the answer is 1785. On dividing 357 by 2, there is 178, and a remainder; you therefore place 5 at the right of the line, and the result is again 1785.

The re is something more curious in the properties of the number 9. Any number multiplied by 9 produces a som of figures which, added together, continually makes 9. For example, all the first multiples of 9, as 18, 27,36, 45, 54, 63, 72, 81, sum up 9 each. Each of them multiplied by any number whatever produces a 6imliar result; as 8 times 81 are 648, these added together make 18, 1 and 8 are 9. Multiply 648 by itself, the product is 419,-904 - the sum of these digits is 27,2 and 7 are 9. The rule is invariable

Take any number whatever and mul tiply it by 9; or any multiple of 9, and the sum will consist of figures which, added together, continually number 9. As 17 X18 = 306, .6 and 3 are 9; 117 x 27 = 3,159, the figures sum up 18. 8 and 1 are 9; 4591 X 72 = 330-552, the figures sum up 18, 8 and 1 are 9. Again, 87,363 X 54 = 4,717,422; added together, the product is 27, or 2 and 7 are 9, and so always. (See 2459.)