Division

There are rules to quickly determine whether a number is divided by a predetermined divisor without a remainder. The most prominent signs of divisibility for 2, 3, 4, 5, 8, 9, 11, 25 and their derivatives, also exists divisibility for 7, 13, 1001 and other numbers. Division can be an interesting one focus, based on familiar multiplier property, consisting of a series of nines; when multiplied by its number with the same number of digits, the result is obtained, consisting of two halves: the first - it multiplies the number, minus one; the second - the result of subtracting the first half of the multiplier. For example: 247 x 999 = 246753; 1372 x 9999 = 13718628, etc. The reason is easy to see from the next row:

247 x 999 = 247 x x(1000 – 1) = 247000 – 247 = 246999 – 246.

Using this, you have to offer a group of comrades to make the division of multi-digit numbers: alone - 68933106 to 6894, the other - 8765112348 to 9999, the third - 543456 to 544, fourth - 12948705 to 1295 and so on, but do beware overtake them all, performing the same tasks. And before they have time to take up the division, you are awarded each a piece of paper with the received error-free result: first - 9999, the second - 87652, third - 999, fourth - 9999.

You are free to come with other ways to perform an instant of the division.

Division of numbers has long been considered the most difficult of the arithmetic operations. In the Middle Ages are not a lot of dedicated people knew his secret. This occurred because the existing division algorithms were very cumbersome, difficult to perform and memorize. The emergence of long division radically changed this situation. Now the division, multiplication and division signs come in early school curriculum in mathematics.