Fast mental calculation tricks

EasyMath

• Editore: MatematicaFacile
• Anno: 2020
• ISBN:
  9791220239127
• Argomento: Matematica
• Categoria: Calcolo

Who wouldn't like to master math naturally, being able to do perform mental calculation without the help of a calculator?
If you had to calculate the square of 115 in a few seconds what would you answer? Or the product 238x5, or even the square of 76?
With this guide you will become masters of fast mental calculation, you will surprise your friends with your skills and you will be astonished when you discover that reaching apparently impossible goals can be achieved with very little effort.

Multiply by 1,5

How do you easily multiply a number by 1,5?

The answer is very simple, just observe that multiplying by 1,5 is equivalent to calculate the half of the triple, or it can be obtained by adding its half to the starting number. Some examples that make use of the first technique are:

12 x 1,5 = (12 x 3) : 2 = 36 : 2 = 18

17 x 1,5 = (17 x 3) : 2 = (10 x 3 + 7 x 3) : 2 = (30 + 21) : 2 = 51 : 2 = (50 + 1) : 2 = 25 + 0,5 = 25,5

74 x 1,5 = (74 x 3) : 2 = (70 x 3 + 4 x 3) : 2 = (210 + 12) : 2 = 222 : 2 = 111

99 x 1,5 = (99 x 3) : 2 = (100 x 3 - 1 x 3) : 2 = (300 - 3) : 2 = 150 - 1,5 = 148,5

The same calculations performed with the second technique:

12 x 1,5 = 12 + (12 : 2) = 12 + 6 = 18

17 x 1,5 = 17 + (17 : 2) = 17 + (10 : 2 + 7 : 2) = 17 + 5 + 3,5 = 22 + 3,5 = 25,5

74 x 1,5 = 74 + (74 : 2) = 74 + (70 : 2 + 4 : 2) = 74 + 35 + 2 = 70 + 30 + 4 + 5 + 2 = 111

99 x 1,5 = 99 + (99 : 2) = 99 + (100 : 2 - 1 : 2) = 99 + 50 - 0,5 = 100 - 1 + 50 - 0,5 = 150 - 1,5 = 148,5

 

Multiply by multiples of 10

Suppose we want to calculate the product of a number and a multiple of 10, for example

12 x 30

where 30 is multiple of 10, in fact

30 = 3 x 10

we can write

12 x 30 = (12 x 3) x 10 = 36 x 10 = 360

We observe that the product between a number and n times 10 can be obtained just calculating the product of the number by n and then multiply the result by 10.

Other explanatory examples:

8 x 50 = (8 x 5) x 10 = 40 x 10 = 400

9 x 90 = (9 x 9) x 10 = 81 x 10 = 810

15 x 40 = (15 x 4) x 10 = (15 x 2 x 2) x 10 = (30 x 2) x 10 = 60 x 10 = 600

24 x 70 = (24 x 7) x 10 = (20 x 7 + 4 x 7) x 10 = (2 x 7 x 10 + 28) x 10 = (14 x 10 + 28) x 10 = (140 + 28) x 10 = 168 x 10 = 1680

81 x 20 = (81 x 2) x 10 = (80 x 2 + 1 x 2) x 10 = (160 + 2) x 10 = 162 x 10 = 1620

 

Multiply by 11, 21, 31, …

Let's see other examples of fast calculations. To multiply a number by 11 just multiply it by 10 and add the number itself, in fact 11 = 10 + 1. Let's see some examples:

23 x 11 = (23 x 10) + 23 = 230 + 23 = 253

40 x 11 = (40 x 10) + 40 = 400 + 40 = 440

88 x 11 = (88 x 10) + 88 = 880 + 88 = 900 - 20 + 80 + 8 = 980 - 20 + 8 = 960 + 8 = 968

145 x 11 = (145 x 10) + 145 = 1450 + 145 = 1450 + 100 + 40 + 5 = 1550 + 40 + 5 = 1590 + 5 = 1595

Similarly, to multiply a number by 21 just multiply it by 20 and add the number itself, in fact 21 = 20 + 1, where, in turn, 20 = 2 x 10.

Examples:

23 x 21 = (23 x 20) + 23 = (23 x 2) x 10 + 23 = 46 x 10 + 23 = 460 + 23 = 483

56 x 21 = (56 x 20) + 56 = (56 x 2) x 10 + 56 = (50 x 2 + 6 x 2) x 10 + 56 = (100 + 12) x 10 + 56 = 1120 + 56 = 1120 + 50 + 6 = 1170 + 6 = 1176

83 x 21 = (83 x 20) + 83 = (83 x 2) x 10 + 83 = (80 x 2 + 3 x 2) x 10 + 83 = (160 + 6) x 10 + 83 = 1660 + 83 = 1660 + 80 + 3 = 1740 + 3 = 1743

The multiplication of a number by 31 (and, similarly, by 41, 51, 61 and so on) ca...