What are some old math tricks
5 math tricks to make dividing and multiplying easier.
Mathematics is rarely very popular. This does not only apply in school, even some adults cannot get used to all the numbers and mental arithmetic and are happy to be able to use pocket calculators. But there are some simple arithmetic tricks and donkey bridges with which young and old math opponents can easily multiply and divide even large numbers without a calculator.
1.) Multiply by 7
As a little learning exercise to internalize the multiplication table of 7, first draw a grid with nine fields, as you know it from the game Tic-Tac-Toe. Enter the numbers one to three from top to bottom in the three fields of the right column; in the middle column the numbers four to six and on the left seven to nine.
Next to it, write down the numbers zero to six on small cards, with two and four appearing twice. The cards can now be assigned to the numbers in the grid. It is noticeable that the cards are arranged horizontally from left to right and from top to bottom in ascending order, while the numbers in the grid are arranged vertically from top to bottom from right to left.
2.) Form a square number
To get the square number, perform two independent calculation steps: In the first step you add the number that is to be multiplied by itself with its last digit. In the second step you multiply the last digit by yourself. The results of these two operations, written one after the other, give the square number.
In this form, however, the trick only works for the numbers 11 to 13 and 104 to 109.
3.) Multiply by 9
With the fingers of your two hands you can access the entire multiplication table for 9. To do this, put your hands in front of you with outstretched fingers. Now count the number you want to multiply by 9 from left to right on your fingers, starting with the thumb of your left hand.
This would be the one, the middle finger of the left hand the three, the little finger of the right hand the six, etc. You bend the corresponding finger. Then count the number of fingers that are left and right of the bent finger.
The number of fingers on the left corresponds to the first digit of the result, the number of fingers on the right corresponds to the second digit. In the example 6 × 9 = 54: Five fingers are on the left and four are on the right of finger no. 6, the little finger of the right hand.
This trick works with numbers of any size: Basically, you draw a table in which each digit of the multiplier has its own column and each digit of the multiplicand has its own row. The fields are then halved diagonally as shown.
In the fields you enter the product of the two numbers that precede the respective column or row. You write down the tens of the result in the left half of the table field and the ones in the right half.
When the table is filled out, you add the numbers that are diagonally to each other and note these sums under the table. The digits read from left to right give the product of the multiplication problem
If the addition of the diagonals results in a two-digit number, you have to add the tens to the result of the addition of the diagonals to the left of it.
5.) Divide by 9
Divide any number, no matter how large, by 9 by making the following notes under the dividend (i.e. the number to be divided): First, write the first digit of the dividend that will remain. In the second place you write down the sum of the first and second digits of the dividend. In the third place you write down the sum of the addition result you just noted and the third digit of the dividend. From then on it goes on and on: The last number noted is added to the next digit of the dividend.
In the end, there is a number left that is the sum of your last noted number and the last digit of the dividend. You divide this remaining number by 9. You add the result to the last digit.
If the numbers you write under the dividend have two digits, add the tens to the number to the left. If the last remaining number is not evenly divisible by 9, you take the remainder times 10 and divide it by 9; you repeat that with the resulting remainder. These are then the decimal places of the final result, which are usually periodic, i.e. infinite.
However, for anyone who - other than mentioned at the beginning - is a math sympathizer, the tricks listed here may offer a little pastime, simply trying out other forms of arithmetic than the usual written multiplication and division, as you know from school. Another well-known math trick is this arithmetic trick from Japan.
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