Many schoolchildren are appalled at the mere mention of the solution of mathematical examples.
Sometimes the calculations seem so complicated that you can not do without a calculator.
But mathematics is a science, although complex, but natural, and with the help of some mathematical techniques one can learn to produce quite complex mathematical actions in the mind.
Multiplication of two-digit numbers by 11.
Anyone who knows the multiplication table, for sureRemembers that it is easiest to multiply the number by 10, because no matter how complex the original number was, only zero will be added to its record at the end. However, multiplying by 11 is also very easy! To do this, you need to add both numbers that make up the given number, and assign the first digit to the left, and the second digit to the right.
31 is the original number.
3 (3 + 1) 1
It turns out 31 * 11 = 341
Do not worry, if you add two digits, you get a two-digit number - just add one to the left digit.
39 is the original number.
3 (3 + 9) 9
3 + 1 2 9
It turns out that 39 * 11 = 429
Multiplication of any number by 4.
One of the most obvious mathematical techniquesIs the multiplication of numbers by 4. To facilitate the work, without multiplying the numbers in the mind, you can multiply the number first by 2 twice in a row, and then add the results.
745 is the original number.
745 * 2 + 745 * 2 = 2980
Thus, 745 * 4 = 2980
Multiplication of any number by 5.
Some people face difficulties when multiplying large numbers by the number 5. In order to quickly multiply the number by 5, you need to split it in half and evaluate the result.
If, as a result of division, an integer is obtained, then it is necessary to assign the number 0 to it.
1348 is the original number.
1348: 2 = 674 is an integer.
Hence, 1348 * 5 = 6740
If the result is a fractional number, then discard all the digits after the decimal point and assign the number 5.
5749 is the original number.
5749: 2 = 2874.5 is a fractional number.
Hence, 5749 * 5 = 28745
The squaring of a two-digit number ending in the figure 5.
When constructing such a number in a square, it is necessary to square up only its first digit, adding one to it, and add 25 at the end of the number.
75 is the original number.
7 * (7 + 1) = 56 Assign 25, and get the result: 75 in the square will be equal to 5625.
The regrouping method, if one of the numbers is even.
If you need to multiply 2 large numbers and one of them is even, you can simply regroup them.
32 must be multiplied by 125
32 * 125 = 16 * 250 = 4 * 1000 = 4000
That is, it turns out that 32 * 125 = 4000