MULTIPLICATION TABLES - REMEMBERING MADE EASY BY SPECIAL TIPS, EASY TO FOLLOW

Your Ad Here



Do you Want to learn Multiplication Tables
by playing a Video game ?
Here is a stunning, high-end video game just for
multiplication!
There's a free version and a premium version.
Give it a try!

Multiplication Tables through Video Game.

Please study the introductory part of
Multiplication
where we discussed the multiplication as repeated addition
with examples and exercises.

There, we also discussed the need to remember
the values of the products of one single digit number
with another single digit number.

Learning these products is much like vocabulary in a language.
Till you master the vocabulary,
the language looks like a foreign language.
Once you master, the language becomes your mother tongue.

Our aim here is to make the single-digits' products
as easy as your mother tongue.

We try to establish the connections between
any two single-digit factors and the resulting product,
until the connection becomes intuitive.

We also provided another page to
help to remember the Multiplication
Table up to 9 x 9 using a simple
principle from Vedic mathematics.
For that page go to
Remembering Multiplication Table
using the principle of Vedic math.

Multiplication Table upto 10 times10

x12345678910
112345678910
22468101214161820
336912151821242730
4481216202428323640
55101520253035404550
66121824303642485460
77142128354249566370
88162432404856647280
99182736455463728190
10102030405060708090100


A multiplication table ("times table") is a grid where
rows and columns are headed by the numbers to multiply,
and the entry in each cell is the product
of the column and row headings.
The heading for the first row and first column contains
the symbol "x" which is multiplication operator.

So, for example, 6 x 8 = 48 by looking up where 6 and 8 intersect.

The traditional rote learning of multiplication was based
on memorization of columns in the table, in a form like


           1 x 8 =  8 
           2 x 8 = 16 
           3 x 8 = 24 
           4 x 8 = 32 
           5 x 8 = 40 
           6 x 8 = 48 
           7 x 8 = 56 
           8 x 8 = 64 
           9 x 8 = 72 
          10 x 8 = 80 

Learning the contents of the (10x10) table is much easier than it superficially seems to be.

Here are some TIPS which are helpful
in remebering the contents of the Table.













Tip 1 of Multiplication Tables :

Half of the table is a mirror image of the other
or Order of Multiplying Does Not Matter.

The entries in the Multiplication Table above and below
the Principal Diagonal Elements are the same.

Because of the symmetry of the Multiplication Table
45 entries are in fact duplicates.
(45 + 10 principal diagonal elemements = 55 entries left).

For Example, If you remember 4 x 7 = 28,
then, you also know the value of 7 x 4.
4 x 7 = 28 = 7 x 4

If you remember 3 x 8 = 24,
then, you also know the value of 8 x 3.
3 x 8 = 24 = 8 x 3

Because of Tip1, it is enough if you remember
half of the Table which is shown below.

x12345678910
112345678910
2 468101214161820
3  912151821242730
4   16202428323640
5    253035404550
6     3642485460
7      49566370
8       647280
9        8190
10         100


Tip 2 of Multiplication Tables :

1 times table and 10 times table are easy to remember.

1 times any number = that number.
10 times any number = that number followed by zero.

For Example,
1 x 5 = 5; 1 x 7 = 7 etc.
10 x 5 = 50; 10 x 7 = 70 etc.

So, no effort is required in remembering
1 times table and 10 times table.

This reduces the entries of the Table
to remember to the following.

x12345678910
1          
2 4681012141618 
3  9121518212427 
4   162024283236 
5    2530354045 
6     36424854 
7      495663 
8       6472 
9        81 
10          


Tip 3 of Multiplication Tables :

We know, the number multiplied by itself
is called the Square of the Number.

The product of the Numbers which differ by 2 is equal to
the square of the in between number minus one.

To apply this Tip, you need to remember
the Squares of the Numbers.

I strongly advise you to remember the
squares of numbers which are given below.

           1  x  1  =   1
           2  x  2  =   4
           3  x  3  =   9
           4  x  4  =  16
           5  x  5  =  25
           6  x  6  =  36
           7  x  7  =  49
           8  x  8  =  64
           9  x  9  =  81
          10  x 10  = 100

Note that these are nothing but
the elements of the principal diagonal.

Now, to apply the above Tip,
consider 7 x 9.
7 and 9 differ by 2.
So their product = 7 x 9
= square of in between number (which is 8) minus 1.
= 8 x 8 - 1 = 64 - 1 = 63.

Let us see another example.
consider 4 x 6.
4 and 6 differ by 2.
So their product = 4 x 6
= square of in between number (which is 5) minus 1.
= 5 x 5 - 1 = 25 - 1 = 24.

With this Tip,
the elements 2 x 4, 3 x 5, 4 x 6, 5 x 7, 6 x 8, 7 x 9
can be remembered and hence the table reduces to

x12345678910
1          
2 46 1012141618 
3  912 18212427 
4   1620 283236 
5    2530 4045 
6     3642 54 
7      4956  
8       6472 
9        81 
10          












Tip 4 of Multiplication Tables :

The product of the Numbers which differ by 4 is equal to
the square of the middle number minus 4.

Now, to apply the above Tip,
consider 4 x 8.
4 and 8 differ by 4.
So their product = 4 x 8
= square of the middle number (which is 6) minus 4.
= 6 x 6 - 4 = 36 - 4 = 32.

Let us see another example.
consider 3 x 7.
3 and 7 differ by 4.
So their product = 3 x 7
= square of the middle number (which is 5) minus 4.
= 5 x 5 - 4 = 25 - 4 = 21.

With this Tip,
the elements 2 x 6, 3 x 7, 4 x 8, 5 x 9
can be remembered and hence the table reduces to

x12345678910
1          
2 46 10 141618 
3  912 18 2427 
4   1620 28 36 
5    2530 40  
6     3642 54 
7      4956  
8       6472 
9        81 
10          


Get The Best Grades With the Least Amount of Effort

Here is a collection of proven tips,
tools and techniques to turn you into
a super-achiever - even if you've never
thought of yourself as a "gifted" student.

The secrets will help you absorb, digest
and remember large chunks of information
quickly and easily so you get the best grades
with the least amount of effort.

If you apply what you read from the above
collection, you can achieve best grades without
giving up your fun, such as TV, surfing the net,
playing video games or going out with friends!

Know more about the

Speed Study System.



Tip 5 of Multiplication Tables :

Remembering Five times table :

5 times even number = half of the even number followed by 0.
5 times odd number = half of the (odd number - 1) followed by 5.

For example,
5 x 6 = half of 6 followed by 0 = 30
5 x 8 = half of 8 followed by 0 = 40

5 x 7 = half of (7 - 1) followed by 5 = half of 6 followed by 5 = 35
5 x 9 = half of (9 - 1) followed by 5 = half of 8 followed by 5 = 45

With this Tip, the table reduces to

x12345678910
1          
2 46   141618 
3  912 18 2427 
4   16  28 36 
5          
6     3642 54 
7      4956  
8       6472 
9        81 
10          


Tip 6 of Multiplication Tables :

Remembering Nine Times Table made easy :

To remember 9 times table,
we follow an easy method
which is explained below.

Put your hands in front of you with your palms facing you.
Your fingers represent the numbers one to ten in an order.

1 = left thumb
2 = left index finger
3 = left middle finger
4 = left ring finger
5 = left little finger
6 = right little finger
7 = right ring finger
8 = right middle finger
9 = right index finger
10 = right thumb

To find 4 x 9 :
Close your fourth finger (left ring finger).
The number of fingers to the left of the closed finger (3)
is the left digit
and to the right of the closed finger (6)
is the right digit.

So the answer is 36.

To find 6 x 9 :
Close your sixth finger (right little finger).
The number of fingers to the left of the closed finger (5)
is the left digit
and to the right of the closed finger (4)
is the right digit.

So the answer is 54.

To find 7 x 9 :
Close your seventh finger (right ring finger).
The number of fingers to the left of the closed finger (6)
is the left digit
and to the right of the closed finger (3)
is the right digit.

So the answer is 63.

To find 9 x 9 :
Close your ninth finger (right index finger).
The number of fingers to the left of the closed finger (8)
is the left digit
and to the right of the closed finger (1)
is the right digit.

So the answer is 81.

With this method you can find any value from 1 x 9 to 9 x 9.

Another method to write 9 times table as a whole is,
For the values from 1 x 9 to 10 x 9,
increase the left digit from 0 to 9 and decrease the right digit from 9 to 0.

This is clear from the following vertical presentation.

           1 x 9 = 09
           2 x 9 = 18
           3 x 9 = 27
           4 x 9 = 36
           5 x 9 = 45
           6 x 9 = 54
           7 x 9 = 63
           8 x 9 = 72
           9 x 9 = 81
          10 x 9 = 90


With this Tip, the table reduces to

x12345678910
1          
2 46   1416  
3  912 18 24  
4   16  28   
5          
6     3642   
7      4956  
8       64  
9          
10          





Great Deals on School & Homeschool Curriculum Books

Tip 7 of Multiplication Tables :

onetwo equals three times four i. e. 12 = 3 x 4.
fivesix equals seven times eight i. e. 56 = 7 x 8.

See the order of the numbers 1, 2, 3, 4, 5, 6, 7, 8.

With this Tip, we can remember 3 x 4 and 7 x 8and hence the table reduces to

x12345678910
1          
2 46   1416  
3  9  18 24  
4   16  28   
5          
6     3642   
7      49   
8       64  
9          
10          










Tip 8 of Multiplication Tables :

Remembering Two times table :

2 times any number = Adding the number to itself.

Adding the single digit number to itself can be done
with the help of fingers, as explained in Addition.

Here the addition is only once and hence can be done easily.

You may use this tip till you are comfortable in
remembering the 2 times table.

With this Tip, the table reduces to

x12345678910
1          
2          
3  9  18 24  
4   16  28   
5          
6     3642   
7      49   
8       64  
9          
10          


With these 8 Tips, the 100 elements in the Table are reduced to a mere 9 elements.

Tip 9 of Multiplication Tables :

Remembering Six times table :

6 times any number = 5 x the number + the number.

Since, we have already seen the Tip (Tip 5) to remember
the 5 times table, we may use that to find 5 x the number
and add the number to get 6 times the number.

For example,
6 x 6 = 6 x 5 + 6 = half of 6 followed by 0 + 6 = 30 + 6 = 36
6 x 8 = 8 x 5 + 8 = half of 8 followed by 0 + 8 = 40 + 8 = 48

6 x 7 = 7 x 5 + 7 = half of (7 - 1) followed by 5 + 7 = half of 6 followed by 5 + 7 = 35 + 7 = 42
6 x 9 = 9 x 5 + 9 = half of (9 - 1) followed by 5 + 9= half of 8 followed by 5 + 9 = 45 + 9 = 54

With this Tip, the table reduces to

x12345678910
1          
2          
3  9    24  
4   16  28   
5          
6          
7      49   
8       64  
9          
10          


With these 9 Tips, the 100 elements in the Table are reduced to a mere 6 elements.

Great deals on School & Homeschool Curriculum Books and Software

Tip 10 of Multiplication Tables :

Applying the Divisibility Rules to the result.

For example, for a number to be divisible by 3
the sum of the digits is to be divisible by 3.

Suppose you write 3 x 8 = 24.
You may check that 2 + 4 = 6 is divisible by 3.

For a number to be divisible by 7,
the difference of two times the last digit and
the remaining number is to be divisible by 7.

Suppose you write 4 x 7 = 28.
You may check that 2 x 8 - 2 = 16 - 2 = 14 is divisible by 7.

Note that all these Tips are only to help
to remember the MultiplicationTables.
If you can directly remember the Multiplication Tables,
these tips are not necessary.

With Tips or without Tips,
you have to remember the Multiplication Tables
upto 9 x 9, accurately.

Put the required time and energy to remember
these Multiplication Tables (1 x 1 to 9 x 9),
without which you can not proceed further
in calculations and in math.

With the help of the above Multiplication table,
you can find the product of any two numbers.

If you still have difficulty,
in remembering the Tables
(1 x 1 to 9 x 9),
Try the Video game mentioned
at the top of this page.

Some students, who have good memory and
good capacity for attention may remember
the Multiplication Tables upto 20 x 20.

If you can also do the same, here is the
Multiplication Table upto 20 times20.

Note that memorising the Multiplication tables
beyond 9 x 9 is optional.

With the knowledge of Multiplication Tables upto 9 x 9
and the knowledge of Multiplication,
you can find the other entries in the following table.

For example, we have found the values of
4 x 12, 6 x 20, 2 x 30, 4 x 15. 4 x 11 and 5 x 13
in Examples 4 to 9 of Multiplication. Multiplication Table upto 20 times20.

x1234567891011121314151617181920
11234567891011121314151617181920
2246810121416182022242628303234363840
33691215182124273033363942454851545760
448121620242832364044485256606468727680
55101520253035404550556065707580859095100
66121824303642485460667278849096102108114120
7714212835424956637077849198105112119126133140
881624324048566472808896104112120128136144152160
9918273645546372819099108117126135144153162171180
10102030405060708090100110120130140150160170180190200
11112233445566778899110121132143154165176187198209220
121224364860728496108120132144156168180192204216228240
1313263952657891104117130143156169182195208221234247260
1414284256708498112126140154168182196210224238252266280
15153045607590105120135150165180195210225240255270285300
16163248648096112128144160176192208224240256272288304320
171734516885102119136153170187204221238255272289306323340
181836547290108126144162180198216234252270288306324342360
191938577695114133152171190209228247266285304323342361380
2020406080100120140160180200220240260280300320340360380400


We will see one more Tip here.



Tip 11 of Multiplication Tables :

Rememebering 11 times Table

11 times single digit = digit twice.
11 times two digit number = sum of the digits between the digits, if the sum of digits is single digit..
If the sum of the digits is double digit, carry over 1 to the left.

For Example,
11 x 6 = 66; 11 xx 8 = 88; 11 x 3 = 33;
11 x 12 = 1 (1 + 2) 2 = 132; 11 x 18 = 1 (1 + 8) 8 = 198;
11 x 19 = 1( + 1) 0 9 = 209;
11 x 89 = 8( + 1) 7 9 = 979;

In 11 x 12, 1 + 2 = 3 is put beteen 1 and 2 to get 132.
∴ 11 x 12 = 132.

In 11 x 19, 1 + 9 =10.
So 1 is carried over to the left and 0 is put between the digits.
The carried over 1 added to the left 1 gives 2.
∴ 11 x 19 = 209.

Progressive Learning of Math : Multiplication tables

Recently, I have found a series of math curricula
(Both Hard Copy and Digital Copy) developed by a Lady Teacher
who taught everyone from Pre-K students to doctoral students
and who is a Ph.D. in Mathematics Education.

This series is very different and advantageous
over many of the traditional books available.
These give students tools that other books do not.
Other books just give practice.
These teach students “tricks” and new ways to think.

These build a student’s new knowledge of concepts
from their existing knowledge.
These provide many pages of practice that gradually
increases in difficulty and provide constant review.

These also provide teachers and parents with lessons
on how to work with the child on the concepts.

The series is low to reasonably priced and include

Elementary Math curriculum

and

Algebra Curriculum.