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

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

x	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42	49	56	63	70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54	63	72	81	90
10	10	20	30	40	50	60	70	80	90	100

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.

x	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2		4	6	8	10	12	14	16	18	20
3			9	12	15	18	21	24	27	30
4				16	20	24	28	32	36	40
5					25	30	35	40	45	50
6						36	42	48	54	60
7							49	56	63	70
8								64	72	80
9									81	90
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.

x	1	2	3	4	5	6	7	8	9	10
1
2		4	6	8	10	12	14	16	18
3			9	12	15	18	21	24	27
4				16	20	24	28	32	36
5					25	30	35	40	45
6						36	42	48	54
7							49	56	63
8								64	72
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

x	1	2	3	4	5	6	7	8	9	10
1
2		4	6		10	12	14	16	18
3			9	12		18	21	24	27
4				16	20		28	32	36
5					25	30		40	45
6						36	42		54
7							49	56
8								64	72
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

x	1	2	3	4	5	6	7	8	9	10
1
2		4	6		10		14	16	18
3			9	12		18		24	27
4				16	20		28		36
5					25	30		40
6						36	42		54
7							49	56
8								64	72
9									81
10

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

x	1	2	3	4	5	6	7	8	9	10
1
2		4	6				14	16	18
3			9	12		18		24	27
4				16			28		36
5
6						36	42		54
7							49	56
8								64	72
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

x	1	2	3	4	5	6	7	8	9	10
1
2		4	6				14	16
3			9	12		18		24
4				16			28
5
6						36	42
7							49	56
8								64
9
10

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

x	1	2	3	4	5	6	7	8	9	10
1
2		4	6				14	16
3			9			18		24
4				16			28
5
6						36	42
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

x	1	2	3	4	5	6	7	8	9	10
1
2
3			9			18		24
4				16			28
5
6						36	42
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

x	1	2	3	4	5	6	7	8	9	10
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.

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.

x	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
1	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
2	2	4	6	8	10	12	14	16	18	20	22	24	26	28	30	32	34	36	38	40
3	3	6	9	12	15	18	21	24	27	30	33	36	39	42	45	48	51	54	57	60
4	4	8	12	16	20	24	28	32	36	40	44	48	52	56	60	64	68	72	76	80
5	5	10	15	20	25	30	35	40	45	50	55	60	65	70	75	80	85	90	95	100
6	6	12	18	24	30	36	42	48	54	60	66	72	78	84	90	96	102	108	114	120
7	7	14	21	28	35	42	49	56	63	70	77	84	91	98	105	112	119	126	133	140
8	8	16	24	32	40	48	56	64	72	80	88	96	104	112	120	128	136	144	152	160
9	9	18	27	36	45	54	63	72	81	90	99	108	117	126	135	144	153	162	171	180
10	10	20	30	40	50	60	70	80	90	100	110	120	130	140	150	160	170	180	190	200
11	11	22	33	44	55	66	77	88	99	110	121	132	143	154	165	176	187	198	209	220
12	12	24	36	48	60	72	84	96	108	120	132	144	156	168	180	192	204	216	228	240
13	13	26	39	52	65	78	91	104	117	130	143	156	169	182	195	208	221	234	247	260
14	14	28	42	56	70	84	98	112	126	140	154	168	182	196	210	224	238	252	266	280
15	15	30	45	60	75	90	105	120	135	150	165	180	195	210	225	240	255	270	285	300
16	16	32	48	64	80	96	112	128	144	160	176	192	208	224	240	256	272	288	304	320
17	17	34	51	68	85	102	119	136	153	170	187	204	221	238	255	272	289	306	323	340
18	18	36	54	72	90	108	126	144	162	180	198	216	234	252	270	288	306	324	342	360
19	19	38	57	76	95	114	133	152	171	190	209	228	247	266	285	304	323	342	361	380
20	20	40	60	80	100	120	140	160	180	200	220	240	260	280	300	320	340	360	380	400

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.

$footer for Multiplication tables page$