Multiplying around the world

Hey MIMU,

I'm teaching multiplication right now to my grade 4 class. Are there any interesting ways of teaching this concept - like different approaches from different cultures?

Signed, 

Multiplication on the Brain

Funny you should ask, Multi! One of our group members, Irma, put together like a zillion different ways of teaching multiplication that are used around the world. Take a peak!

Multiplication in different civilizations:

      Multiplication (often denoted by the cross symbol (x), or aside the absence of a symbol) is the third basic mathematical operation of arithmetic. The  generation of two solid numbers is equivalent to the addition of one of them by itself as many times as the value of the other one. For instance, 4 multiplied by 5

4 x 5  = 4+4+4+4+4= 20

Here 4 and 5 are the factors and 20 is the product. One of the principal properties of that, the result result does not depend on the position of the factory and is commutative property. For instance, 4 multiplied by 5 can also be calculated by adding 4 copies of 5  together

4 x 5 = 5 + 5 + 5+ 5 = 20

The common methods for multiplying numbers using pencils and paper require a multiplication table of memorized or consulted products of small numbers, however one method, the peasant multiplication algorithm does not. Modern electronic computers and calculators have greatly cut down the need for multiplication by hands. Methods of  multiplication were documented in the Egyptian, Greek, Indian and Chinese cultures. The computation is enabled by applying several methods: by memory, in writing or using calculation devices like in ancient stones, abacus and in modern like calculators.

Chinese stick multiplication: Most people multiply numbers by the arrangement of digits and carrying of numbers such as in the figure below for the multiplication of  22 and 41

 22                                       

x41                                      

 22

88x

902

The chinese used different method in which sticks were used to represent the digits of each number and then the intersections of these sticks were counted in a specific way in order to get the correct product.

For instance,   4 x 3 =12

In this example, the four pink lines represent 4 and three green lines represent 3 and for the product only to count orange lines. Finally we get 12.

Lets try some more with numbers which have tens

16 x 24 =  384

  

For this example, 16 has one green stick which represent the tens digit and a group of six represent the

ones digits. For 24, it has 2 purple sticks which represent the tens digit and four sticks represent the ones digit. The intersection of the ones. There are 24 intersection so just like multiplication need to carry the 2 over to our tens digit  and in pink circle from the intersection of from the two cases of a ones digit and with a tens digit. Here we have only 16 intersections in the pink circle, but we have to carry two from the ones digit so, we have to two from the ones digit so now its 18. In orange we have two intersections and need to carry one from the previous tens digit so now its 3 for hundreds digit , so now, we have 384 as a product.

Overall, the chinese stick multiplication ensures that the person who is performing the multiplication understands the base 10 system and the effect that each digit has during the multiplication.    

Finger multiplication method:

The use of finger multiplication is the traditional method and if kid has some difficulty in remembering the multiplication tables then it can be good alternative for them. Here is a technique:

The two numbers to be multiplied are each represented on a different hands. Label our both fingers from 6 to 10 and then each hand may have some raised fingers and and close fingers at the same time. The sum of the raised finger is the number of tens and product of the closed finger is the number of the ones.

for instance,   

6 x 8

For 6 , use your left hand and raise 1 finger and this means there are 4 closed fingers.

For 8, use  your right hand and raise 3 fingers and this means there are 2 closed fingers.

Sum of raised fingers= 1+ 3 =4 which means we have 4 tens or 40

Sum of the closed fingers   4 x2 = which we have 8 ones

40 + 8 = 48

Vedic multiplication method:

Vedic multiplication is an ancient technique which is based on the veda. Vedas are the set of sacred ancient Hindu  texts. In 1965, a book titled Vedic mathematics was published in English and was written by Bharati Krishna Tirthaji. It contains a list of mental calculation techniques claimed to be based on the vedas

Multiplying by 11:

To multiply any number by 11 do the following :

Working from right to left

Write the rightmost digit of the starting number down.

Add each pair of digits and write the result down

Finally right down the left most digit. This all shown in above example.

Multiplying two numbers close to 100:

When the technique is extended to double digit numbers, you subtract each from 100 during the vertically stage.

multiply  99 x 98

 99     -01 (100-99)

 98     -02 (100-98)

97        02

multiply  89 x 97

  89    11 (100-89 =11)

  97    3  (100-97 = 3

  86    33

multiply   97x 79

  97    3  ( 100-97)  = 3

  79    21( 100-79) = 21

  76    63

Multiply numbers not close to one hundred:

Write down your numbers sitting on the top of each other, like you would do when multiplying normally. Multiply the numbers in the ones place and put the product directly under the ones. Cross multiply like you would for fractions by taking the top numbers tens digit multiplied by the bottom numbers one place. Then take the bottom numbers one place multiplied by the bottom numbers tens place. add the two products and place the answer to the left of the ones places answer. Multiply the numbers in the tens place the answer to the left of the previous step’s answer.

For example:

  21( cross multiply)  2x3=  6

x23 (cross multiply ) 2 x 1=2

483                                   8                           

Square of digits:

Square of numbers ending with 5

Formula for calculating square ending with 5 is easy. I have also discussed this multiplication in my multiplication Article

   85

 x85

7225

  

Steps :

Multiply 5 by 5 and put composite digit 25 on the right hand side.

Add 1 to the upper left hand side digit i. e. 8 i. e. 8+1=9

Multiply 9 to the lower hand digit 8, i. e. 9x8=72

Our answer is 7225

Using this method we can find out square of the number. Now let’s have a look at method of calculating square of adjacent number.

     75

   x75

 5625