Trucos de Mates (traducción en progreso)

Estos trucos de mates son de los Vedas, los libros más antiguos conocidos por la Humanidad.

parte1

Usar la fórmula todos de 9 y el último de 10 para realizar restas en un instante.

• Por ejemplo 1000 – 357 = 643 . Restamos cada cifra en 357 de 9 y la última cifra de 10.
• La respuesta es 1000 – 357 = 643¡Y eso es todo!Esto funciona con números que consisten de 1 seguido de ceros: 100; 1000; 10,000 etc. En el caso de otra cifra diferente al 1, sólo hay que restarle 1 al resultado
• Similarmente 10,000 – 1049 = 8951
• Para 1000 – 83, en el cual tenemos más ceros que cifras en los números que se restan, sencillamente suponemos que 83 es 083. Así 1000 – 83 se vuelve 1000 – 083 = 917

parte 2

Usando VERTICALMENTE Y CRUZADO sólamente necesitas hasta la tabla del 5.

• Supongamo que queremos 8 x 7, 8 está 2 por debajo de 10 y 7 está 3 por debajo de 10. Piensa así:
• La respuesta es 56. El diagrama de abajo muestra como hacerlo.Restamos cruzado 8-3 ó 7 – 2 para obtener 5,

  la primera cifra de la respuesta.

  Y multiplicas verticalmente: 2 x 3 para obtener 6,

  la última cifra de la respuesta.

  Eso es todo:

  Mirar cuán por debajo de 10 esta el número, restar la deficiencia del número por el otro número, y multiplicar las deficiencias.

• 7 x 6 = 42 Aqui «nos llevamos»el «1» del «12» que convierte el 3 en 4.

Here’s how to use VERTICALLY AND CROSSWISE for
multiplying numbers close to 100.

• Suppose you want to multiply 88 by 98.

  Not easy,you might think. But with

  VERTICALLY AND CROSSWISE you can give

  the answer immediately, using the same method

  as above.

  Both 88 and 98 are close to 100.

  88 is 12 below 100 and 98 is 2 below 100.

  You can imagine the sum set out like this:

  

  As before the 86 comes from

  subtracting crosswise: 88 – 2 = 86

  (or 98 – 12 = 86: you can subtract

  either way, you will always get

  the same answer).

  And the 24 in the answer is

  just 12 x 2: you multiply vertically.

  So 88 x 98 = 8624

This is so easy it is just mental arithmetic.

Multiplying numbers just over 100.

• 103 x 104 = 10712The answer is in two parts: 107 and 12,107 is just 103 + 4 (or 104 + 3),and 12 is just 3 x 4.
• Similarly 107 x 106 = 11342107 + 6 = 113 and 7 x 6 = 42

Again, just for mental arithmetic

parte 3

The easy way to add and subtract fractions.

Use VERTICALLY AND CROSSWISE to write the answer straight down!

• 

Multiply crosswise and add to get the top of the answer:

2 x 5 = 10 and 1 x 3 = 3. Then 10 + 3 = 13.

The bottom of the fraction is just 3 x 5 = 15.

You multiply the bottom number together.

So:

• Subtracting is just as easy: multiply crosswise as before, but
  the subtract:
• 

parte 4

A quick way to square numbers that end in 5 using
the formula BY ONE MORE THAN THE ONE BEFORE.

• 75² = 5625 75² means 75 x 75.The answer is in two parts: 56 and 25.The last part is always 25.The first part is the first number, 7, multiplied by the number
  «one more», which is 8:so 7 x 8 = 56
• Similarly 85² = 7225 because 8 x 9 = 72.

Method for multiplying numbers where the first
figures are the same and the last figures add up to 10.

• 32 x 38 = 1216

Both numbers here start with 3 and the last

figures (2 and 8) add up to 10.

So we just multiply 3 by 4 (the next number up)

to get 12 for the first part of the answer.

And we multiply the last figures: 2 x 8 = 16 to

get the last part of the answer.

Diagrammatically:



• And 81 x 89 = 7209

We put 09 since we need two figures as in all the other examples.

parte 5

An elegant way of multiplying numbers using a
simple pattern.

• 21 x 23 = 483

This is normally called long multiplication but

actually the answer can be written straight down

using the VERTICALLY AND CROSSWISE

formula.

We first put, or imagine, 23 below 21:



There are 3 steps:

a) Multiply vertically on the left: 2 x 2 = 4.

This gives the first figure of the answer.

b) Multiply crosswise and add: 2 x 3 + 1 x 2 = 8

This gives the middle figure.

c) Multiply vertically on the right: 1 x 3 = 3

This gives the last figure of the answer.

And thats all there is to it.

• Similarly 61 x 31 = 1891



• 6 x 3 = 18; 6 x 1 + 1 x 3 = 9; 1 x 1 = 1

Multiply any 2-figure numbers together by mere
mental arithmetic!

If you want 21 stamps at 26 pence each you can

easily find the total price in your head.

There were no carries in the method given above.

However, there only involve one small extra step.

• 21 x 26 = 546

The method is the same as above

except that we get a 2-figure number, 14, in the

middle step, so the 1 is carried over to the left

(4 becomes 5).

So 21 stamps cost £5.46.

• 33 x 44 = 1452

There may be more than one carry in a sum:



Vertically on the left we get 12.

Crosswise gives us 24, so we carry 2 to the left

and mentally get 144.

Then vertically on the right we get 12 and the 1

here is carried over to the 144 to make 1452.

Any two numbers, no matter how big, can be

multiplied in one line by this method.

parte 6

Multiplying a number by 11.

To multiply any 2-figure number by 11 we just putthe total of the two figures between the 2 figures.
• 26 x 11 = 286Notice that the outer figures in 286 are the 26being multiplied.And the middle figure is just 2 and 6 added up.
• So 72 x 11 = 792

• 77 x 11 = 847This involves a carry figure because 7 + 7 = 14we get 77 x 11 = 7₁47 = 847.

• 234 x 11 = 2574We put the 2 and the 4 at the ends.We add the first pair 2 + 3 = 5.and we add the last pair: 3 + 4 = 7.

parte 7

Method for diving by 9.

• 23 / 9 = 2 remainder 5The first figure of 23 is 2, and this is the answer.The remainder is just 2 and 3 added up!
• 43 / 9 = 4 remainder 7The first figure 4 is the answerand 4 + 3 = 7 is the remainder – could it be easier?

• 134 / 9 = 14 remainder 8The answer consists of 1,4 and 8.1 is just the first figure of 134.4 is the total of the first two figures 1+ 3 = 4,and 8 is the total of all three figures 1+ 3 + 4 = 8.

• 842 / 9 = 8₁2 remainder 14 = 92 remainder 14Actually a remainder of 9 or more is not usuallypermitted because we are trying to find howmany 9’s there are in 842.Since the remainder, 14 has one more 9 with 5left over the final answer will be 93 remainder 5