Multiplication Charts (86)

It was Pythagoras, a renowned mathematician and philosopher from ancient Greece, who came up with the idea to organize the multiplication tables within a chart, hence the name « Pythagorean Table » often used to refer to the Multiplication tables Chart. The Pythagorean table is very useful for quickly finding the result of a multiplication.
Born around 570 BC, he is best known for Pythagoras' theorem, which states the relationship between the lengths of the sides of a right-angled triangle. Pythagoras is often referred to as "Pythagoras of Samos" to indicate his birthplace, the island of Samos, a Greek island located in the Aegean Sea. This island contributed to the intellectual and cultural environment of Pythagoras during his youth, but later in his life, he moved to southern Italy where he established his school called Pythagoreanism. He had a significant impact on philosophy, mathematics, and science.
*The illustration opposite was isolated from a photo of the giant fresco "The School of Athens" by the Italian painter Raphael.

The diagonal of the multiplication table is formed by the cells where the row number equals the column number. The numbers on the diagonal represent the square numbers. A square number is the result of a multiplication where the number is multiplied by itself. For example, 36 is the square of the number 6 because 6 x 6 = 36. In terms of notation, 6 x 6 is equivalent to 6². Verbally, 6² is pronounced as "6 squared" or "6 to the power of 2", it means the same thing.

To illustrate this, we have chosen a colored chart to help you visualize the diagonal. In this example, the diagonal starts from the top left at the number 1 (the square of 1) and goes down to the bottom right at the number 144 (the square of 12).

Here are some tips for adding color to your chart:
Color the cells of the table using your favorite colors! Choose a different color for each of the times tables, this is what we call a color code. This color will be used both vertically and horizontally.

Let's take a concrete example:
If you assign green to the number 3, you should color the following cells in green: 3x3, 3x4, 3x5, 3x6, 3x7, 3x8, 3x9 (horizontal row) as well as 4x3, 5x3, 6x3, 7x3, 8x3, 9x3 (vertical column). As 3x2 belongs to the 2 times table, color it with the color of the 2 times table. The result of 3x2 is equal to the result of 2x3, so it's unnecessary to learn both. When you know the result of the first multiplication, you know the result of the second.
Note: It is not necessary to color the cells corresponding to the 1 and 10 times tables; these multiplications are very easy, and you will remember them without any problem!

A chart 1-10 (or 10x10), contains 100 squares, so 100 results. It may seem like a lot, but... Great news! You will see that there are many squares that you do not need to learn :) In fact, there are 36 multiplications to know or even only 28 multiplications using tricks. Find below the results of the multiplication chart that you don't need to learn.

1- Don't learn duplicates

As we've already discussed above, thanks to the commutative property of multiplication, there are many equivalent multiplications in a chart (in a multiplication, we can interchange the numbers and still obtain the same result). Thus, we observe symmetry on either side of the diagonal. We can therefore remove all the results below the diagonal.
Once these duplicates are removed, there are only 55 multiplications left and you'll see that we can further reduce this number.

2- No need to learn by heart the 1 and 10 times table

The 1 times table and the 10 times table are the 2 easiest, it is therefore useless to learn them by heart.
1 times Table: A number multiplied by 1 is always equal to the number.
Example: 1x1=1, 1x2=2, 1x3=3, 1x4=4...
10 times Table: A number multiplied by 10 is always equal to the number followed by a zero.
Example: 1x10=10, 2x10=20, 3x10=30, 4x10=40...
And there you have it! You can see that there are only 36 multiplications to learn . That's some good news, isn't it? :)

Note: Don't tell your math teacher, but you can even reduce this number to 28 multiplications if you use the finger trick for the 9 times table.

3- And what about a 12 x 12 chart ?

In a multiplication Chart 1-12, there are 144 results. Once all the duplicates (as well as the 1 and 10 times tables) are removed, there are only 55 multiplications left to know.

Note: Here too, we can further reduce this number because there are tricks for the 9, 11 and 12 times tables. Once the multiplications for these three times tables are removed, there are truly only 28 multiplications to know by heart.

At last, a fun and motivating way to practice the times tables without getting bored! Our multiplication games are highly effective for memorizing the tables. They will allow you to progress quickly, and what's more, to motivate you, your efforts will be rewarded with surprise games included in the main game.

Try our online exercises, a simple and effective revision method! The progress bar located above the exercise shows you where you are in the series and the number of mistakes you have made. Below the exercise, your most frequent errors are displayed, which will allow you to know the multiplications that still challenge you.
Choose the multiplication table you want to practice with:

• 2 Times table
• 3 Times table
• 4 Times table
• 5 Times table
• 6 Times table
• 7 Times table
• 8 Times table
• 9 Times table
• All the times tables
  
  

You may have already heard of Flash Cards. These are cards with a question on the front and the answer on the back. Here, the question will be the multiplication, and the answer will be the result of this multiplication. We offer you multiplication table flashcards that you can use as a game. These cards will help you quickly memorize your tables while having fun with your friends.

To practice your times tables, you can also fill in a blank (or empty) multiplication chart This is also an effective technique for long-term memorization of the tables. We offer you a wide selection of printable blank charts (PDF) in A4 format.

The use of dedicated worksheets for multiplication tables proves to be an effective and proven learning method. The worksheets are specially designed to target specific multiplication tables. This will allow you to focus on one table at a time, thus facilitating memorization.
You can find our multiplication exercises here:

• 2 times Table
• 3 times Table
• 4 times Table
• 5 times Table
• 6 times Table
• 7 times Table
• 8 times Table
• 9 times Table
• All times Tables