Many students are horrified at the mere mention of solving mathematical examples.

Sometimes it seems so complex calculation that can not do without a calculator.

But mathematics - a science, though complicated, but a regular, and with the help of some mathematical techniques you can learn to perform fairly complex mathematical operations in mind.

instructions

1

Multiply two-digit numbers to 11.

Anyone who knows the multiplication table, for sureremember that the easiest way to multiply the number by 10, because no matter how complex the original number was not, to his record just added a zero to the end. However, multiply by 11, it is also very easy! To do this, add up the two numbers that make up the given number, and their sum attributed to the first digit on the left and on the right - the second.

Example:

31 - the original number.

3 (3 + 1) 1

It turns out 31 * 11 = 341

Do not worry if the addition of two numbers you got a two-digit number - simply add one digit to the left.

Example:

39 - the original number.

3 (3 + 9) 9

3 + 1 2 9

It turns out 39 * 11 = 429

2

Multiplying any number 4.

One of the most obvious mathematical techniquesis the multiplication of numbers on 4. To facilitate the works, not by multiplying the number in mind, you can multiply the number of first 2 twice in a row, and then add up the results.

Example:

745 - the original number.

745 * 2 + 745 * 2 = 2980

Thus, 745 * 4 = 2980

3

Multiplying any number 5.

Some people experience difficulties when multiplied by the large number in the figure 5. In order to quickly multiply the number by 5, it is necessary to divide it in half, and evaluate the result.

If the result of the division turned an integer, it is necessary to attribute to it the number 0.

Example:

1348 - the original number.

1348: 2 = 674 - integer.

So, in 1348 * 5 = 6740

If as a result of the division turned a fractional number, then drop all the digits after the decimal point, and assign the number 5.

Example:

5749 - the original number.

5749: 2 = 2874.5 - a fractional number.

So, 5749 * 5 = 28745

4

Squaring two-digit number ending in the number 5.

With the construction of such numbers in a square to be squared only the first digit of its previously adding one to it, and at the end of 25 finish.

Example:

75 - the original number.

7 * (7 + 1) = 56 25 Attributed to, and get the result: 75 squared is equal to 5625.

5

Method regrouping if one of the numbers - even.

If you need to multiply two large numbers and at the same time one of them is even, you can just rearrange them.

Example:

32 must be multiplied by 125

32 * 125 = 16 * 250 = 4 * 1000 = 4000

That is, it turns out that 32 * 125 = 4000