This method is as valid as the “Multiplication Tables”, but it is more interesting and mysterious!
In the times tables, you memorize the results of a series of addition operations.
In this system, you memorize a combination of mini-rules that will yield the results.
“look at the number”
“take the number”
“double the number”
“if it is odd, add five”
“add half the previous number (always without the fraction)”
“add the whole previous number”
“subtract from ten”
“subtract from nine”
“double the result”
“subtract one or two from the last number”
“subtract one or two from half the last number”.
The algorithm for each multiplier uses a combination of some of these rules.
Look for the similarities as you learn the system.
The rules for 0, 1 and 2 resemble each other in simplicity. You know these already.
The rules for 5, 6 and 7 resemble each other in the steps. These are the next simplest ones.
The rules for 3 and 4 resemble each other in the steps and they resemble the rules for 8 and 9.
The rules for 8 and 9 resemble each other in the steps.
If you wish to understand more about how this system works, go to Algebra. The keys to understanding the system can be found in Algebra. This will deepen your understanding of Mathematics.
Tells the history of Professor Jakow Trachtenberg.
This true history can be an inspiration to persevere despite tremendous obstacles and hardships.
Presents a multiplication problem and lets you practice this method.
Click on Work Page.
This will open the work page.
Click on the left hand digit of the Multiplicand.
Enter a four digit number as the Multiplicand.
This can be any four numbers.
We recommend that you start with a simple number like 2222 or 3333.
Enter a single digit Multiplier.
We recommend that you start with 5.
The rule for five is an easy one for beginners.
Try this order for ease of learning: 5,6,7,8,9,3,4.
The rules for 1 and 2 you already know. Try them - you’ll see.
The Cursor will be placed in the Product fields.
At this point, read the rules and follow the advice below the product. They will guide you through solving the problem and learning the method. Practice the rule for each multiplier till you remember it as well as the times table.
Once you have solved the problem, you can use the TAB key to move back once the product is in place if you wish to review your steps.
After solving the problem, you can enter another multiplicand without changing the multiplier. That way you can practice the rule for your chosen multiplier with many different multiplicands. Use the TAB key to move the cursor to the multiplicand and then to the multiplier. and then to the first number of the product (the answer).
Incorrect answer numbers are not accepted. If the number you type into the product field does not appear, it is not correct. Read the rules and guidelines carefully and try again.
The step by step guidance displays advice on each step of the problem.
This is the box just below the product fields.
The entire algorithm is visible below the step by step guidance box.
Displays the actual product (the answer) to the right of the fields that accept the product.
You can check it to show the answer while you work.
Click on it again to uncheck it and remove the answer.