The Multiplication Tables

What is a multiplication table?

Multiplication tables are one of the most important topics when learning mathematics, if not the most important, because it is the basis for many other subjects. When dealing with multiplication tables, we must first understand what lies behind the concept of multiplication.

A multiplication table is a table consisting of 10 10 rows and 10 10 columns, each numbered from 1 1 to 10 10 in ascending order to the right and downward. This table concentrates in itself all the multiplications of the numbers from 1 1 to 10 10 .

To find the result derived from the multiplication of two numbers, we must first locate the corresponding column and row. For example: 2×4 2\times4 .

To begin, we must find the column corresponding to the number 2 2 and then the row corresponding to the number 4 4 . The point where the two numbers meet shows the result. According to the table below, the result is 8 8 .

There are many types of multiplication tables but the basic table is from 1 to 10.

multiplication table, 2 times 4

What is a multiplication?

Multiplication is a repeating sum.

For example:

The operation 3×4 3\times4 can be changed to 3+3+3+3 3+3+3+3 , i.e. 4 4 times 3 3 . The result is 12 12 .

Another example:

The operation 7×2 7\times2 can easily be changed by 7+7 7+7 , i.e. 2 2 times 7 7 . The result is 14 14 .


Multiplication tables from 1 to 10

Tabla de multiplicar, 2 por 4

It should be noted that the order of the numbers is of no importance.

For example:

in the case of 2×4 2\times4 , if, instead of doing the search explained in the previous paragraph, we search the column corresponding to the number 4 4 and the row corresponding to the number 2 2 , the result will still be 8 8 .
In other words: 2×4=4×2=8 2\times4=4\times2=8 .

Let's look at another example:

9×7 9\times7 . We look for the column corresponding to the number 9 9 and the row corresponding to the number 7 7 . The point where both meet shows us the number 63 63 , which is the answer to the operation.

Tabla de multiplicar, 9 por 7

Also here we can see that, if we do it the other way around, i.e. 9×7 9\times7 , the result will still be 63 63 .

Tricks for remembering the multiplication tables

There are many children and even adults who find it difficult to memorize the multiplication tables, but luckily there are many tricks that make this task easier.


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Multiples of 1

When we multiply any number by 1 1 it stays the same.

For example, when we multiply any number by :

1×6=6×1=6 1\times6=6\times1=6 .


Multiples of 2

When we multiply any number by 2 2 , what we are actually doing is adding it to itself, i.e., 6×2 6\times2 equals 6+6 6+6 , which equals 12 12 .


Multiples of 3

First, we write the numbers 0 0 , 1 1 and 2 2 as follows:


0......0......0 ......0
1........1.......1
2......2......2

Secondly, we add the digits 1 1 - 9 9 as follows: ascending from the bottom row of the right column to the top row of the same column. Following the order, we do the same in the middle column and in the left column up to the top row of the left column. We would obtain the following table:

03......06......09

12.......15.......18

21......24......27

We thus obtain the multiples of 3 3 :

3×1=3 3\times1=3 ; 3×2=6 3\times2=6 ; 3×3=9 3\times3=9 , etc.


Multiples of 4

This time we must use our hands. We divide each of the fingers into three parts, the fourth part being the area where the finger meets the palm of the hand. At first it helps to put the numbers in each part, from bottom to top, but with practice we will learn it by heart. When we want to calculate, for example, how much is 4×3 4\times3 , what we have to do is to advance to the fourth part of the third finger, where we will have the number 12 12 .


Multiples of 5

This is a fairly easy table, as we can observe a clear pattern in it. If we write the results of the table of 5, we can see how there is a recurring rule:

1×5=5 1\times5=5

2×5=10 2\times5=10

3×5=15 3\times5=15

4×5=20 4\times5=20

5×5=25 5\times5=25

6×5=30 6\times5=30

7×5=35 7\times5=35

8×5=40 8\times5=40

9×5=45 9\times5=45

10×5=50 10\times5=50

If we look at the first digit of each result, we will see that, except for the first 0 0 and the 5 5 that appears at the end, the rest of the digits always appear twice. In addition, we can see that the results end alternately in 0 0 and 5 5 .


Multiples of 6

The simplest method to learn this table is to resort to the table of 5 5 and add to it the number we have multiplied, that is, to obtain the answer to 6×8 6\times8 , we first calculate how much is 5×8 5\times8 , which will give us 40 40 as a result; secondly, to this number we add 8 8 and we will obtain the result corresponding to 6×8 6\times8 ; that is, 48 48 .


Multiples of 7

This time we use a new table and write down the numbers from 1 1 to 9 9 from right to left as follows:

1........4.......7

2.......5.......8

3.......6.......9

Now we add, from left to right, the digits from the 1 1 to 9 9 . In the left column, we write the figures 1 1 , 2 2 y 3 3 from top to bottom; in the middle column, we write the digits 4 4 , 5 5 y 6 6 from top to bottom, and, in the right column, we write the figures 7 7 , 8 8 y 9 9 from top to bottom as well. We obtain the following:

21........14........07

42.......35.......28

63.......56.......49

Now we have in front of us the results of the table 7 from 1 to 9 9 :

7×1=7 7\times1=7 , 7×2=14 7\times2=14 , 7×3=21 7\times3=21 , etc.


Multiples of 8

There is a very simple trick that allows us to find out which are the multiples of 8 8 . First, we arrange the numbers in two rows as follows:

0.......1.......2.......3.......4

5.......6.......7.......8.......9

Then, in each column we add from right to left the even numbers, i.e.: 0 0 , 2 2 , 4 4 , 6 6 and 8 8 .

08.......16......24......32......40

48......56......64......72......80

Thus we get the multiples of 8 8 :

8×1=8 8\times1=8 , 8×2=16 8\times2=16 , 8×3=24 8\times3=24 , etc.


Multiples of 9

To use this trick we must resort to our hands. An important detail that we must take into account is that to the big finger of the left hand we will assign the number 1 1 and to the one of the right hand the number 10 10 . Here we illustrate this statement with a simple example: 9×5 9\times5 .

We count from left to right up to the fifth finger and bend it. This finger will act as a guide.

Then we have to ask ourselves two questions:

How many fingers are in front of the finger we have bent? 4 4

How many fingers are behind the finger we have bent? 5 5

In this simple way we have obtained the answer corresponding to 9×5 9\times5 , i.e. 45 45 .


Multiples of 10

This time no calculation is needed, just add a 0 to the number we have multiplied by 10 10 .

For example: 8×10=80 8\times10=80 , 6×10=60 6\times10=60 .

Phases in the memorization of the multiplication tables

The tricks that we have shown above are especially important in the initial phase to make easier the task of memorizing the multiplication tables, although the main objective is that we know them by heart and we do not have to be calculating the multiples all the time.

The method we recommend is to focus, at first, on the simplest multiples, that is, those of 1 1 , 2 2 , 5 5 and 10 10 . Then, we recommend to include every couple of days a new table to the ones we have already memorized in order to learn them in an easy and progressive way.


Multiplication table exercises

3×3=9 3\times 3=9

7×8=56 7\times 8=56

9×6=54 9\times 6=54

5×8=40 5\times 8=40

4×9=36 4\times 9=36

3×9=27 3\times 9=27

9×5=45 9\times 5=45

6×6=36 6\times 6=36

8×3=24 8\times 3=24

8×8=64 8\times 8=64

6×8=48 6\times 8=48

9×7=63 9\times 7=63

6×2=12 6\times 2=12

3×7=21 3\times 7=21


If you are interested in other areas of multiplication you may be interested in the following articles:

In Tutorela you will find a variety of articles about mathematics.


Trick to multiply numbers with two digits

Printable multiplication tables

Tablas de multiplicar para imprimir

Riddle with multiplication