Many school students are terrified at only one mention of the solution of mathematical examples. Time of calculation seem so difficult that not to do without calculator. But mathematics - science though difficult, but natural, and by means of some mathematical receptions it is possible to learn to make rather difficult mathematical operations in mind.
Instruction
1. Multiplication of two-digit numbers on 11. The one who knows the multiplication table for certain remembers that the easiest to increase number by 10, what difficult the initial number would not be, zero will only be added to its record at the end. However it is very easy to multiply by 11 too! For this purpose it is necessary to put both figures of which this number consists, and to their sum to attribute the first figure at the left, and on the right - the second. Example: 31 - initial number. 3 (3+1) 1poluchayetsya 31*11=341ne it is worth worrying if at addition of two figures at you the two-digit number turned out - just add unit to the left figure. Example: 39 - initial number.3 (3+9) 93+1 2 9poluchayetsya 39*11=429
2. Multiplication of any number on 4. One of the most obvious mathematical receptions is multiplication of numbers on 4. To facilitate works, without multiplying number in mind, it is possible to increase number at first by 2 twice in a row, and then to put results. Example: 745 - initial number.745*2+745*2=2980takim in the way, 745*4=2980
3. Multiplication of any number on 5. Some people meet difficulties with multiplication large number on figure 5. Quickly to increase number by 5, it is necessary to halve it and to estimate result. If as a result of division the integer turned out, then it is necessary to attribute to it figure 0. Example: 1348 - initial number.1348:2=674 - an integer. Means, 1348*5=6740esli as a result of division the fractional number turned out, reject all figures after a comma and attribute figure 5. Example: 5749 - initial number.5749:2=2874.5 - fractional number. Means, 5749*5=28745
4. Squaring of the two-digit number terminating on figure 5. At construction of similar number in a square it is necessary to square only its first figure, previously having added to it unit, and at the end of number to add 25. Example: 75 - * (7+1)=56 we Attribute initial number.7 25, and we receive result: 75 in a square it will be equal to 5625.
5. A way of a regrouping, if one of numbers - even. If you need to increase 2 large numbers and at the same time one of them is even, then it is possible just to rearrange them. Example: 32 it is necessary to increase on 12532*125=16*250=4*1000=4000to is, leaves that 32*125=4000