Receptions of the fast account allow to carry out some calculations, without resorting to the help of the calculator. Having mastered them, you will be able not only to surprise friends and colleagues, but also to use these receptions in practice when performing calculations.

## Instruction

1. Learn to multiply digits by 11, 111, 1111 and so on quickly. For this purpose just replace in these numbers unit with that figure of which the digit consists. For example, 1111*4=4444.

2. On 11 it is possible to multiply in mind and two-digit numbers. For this purpose at first put both figures of two-digit number. For example, at number 43 at addition of figures 4 and 3 7 will turn out. Place result between figures of two-digit number: 473. If the sum of figures turns out more than 10 inclusive, act in a different way. So, at multiplication by the 11th of 48 at addition of figures 4 and 8 12 will turn out. To the senior category of two-digit number add unit: 4+1=5. It will be the senior category of the work. The younger category of the sum - 2, and younger - the younger category of two-digit number, that is, 8 will become its average category. Thus, 48*11=528.

3. To increase number by five, in the beginning increase it by ten, having added zero on the right. For example: 82*10=820. Then divide result into two: 820/2=410. From this it follows that 82*5=410. Both actions combined (multiplication by ten and division into two) can be executed in mind much quicker, than multiplication by five in one action.

4. If you have to work with computer facilities, the nobility of degree of number 2 follows by heart as the multiplication table. Be not too lazy to learn the following number sequence: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576. These are values of degrees of number 2 in the range from 0 to 20.

5. Use approximate calculations where requirements to the accuracy of result are low. It will allow to reduce mathematical operations with multidigit numbers to the same actions with numbers of smaller length. Learn to use a slide rule, and first of all - to multiply and divide on it. For multiplication combine unit on B scale with the first multiplier on A scale. Opposite to the second multiplier on a scale of B there will be a work on A scale. For division combine a dividend on A scale with a divider on B scale. Opposite to unit on a scale of B there will be A, private on a scale. Having brought these actions to automatism, you will be able to multiply and divide numbers from two or three categories quicker, than on the calculator.

6. At calculation of quantity of objects or events use the following reception. Counting the first, second, third or fourth object, draw the parties of a square, and at emergence of the fifth object cross out it. Then begin a new square. After twenty squares (that corresponds to hundred objects or events) begin a new line. Then at first count quantity of full lines - it will be equal to number of hundreds. In the remained incomplete line count the number of couples of squares - it will be number of dozens. In the remained incomplete couple of squares count the number of lines, and the number of units will turn out.