What's the purpose of the Trachtenberg system?

To find an answer 1 digit at a time.

To find an answer in 10 seconds.

To find an answer in a matter of seconds.

To find an answer 3 digits at a time.

What should guarantee the procedure to be effective?

To keep each stage of the operation distinct.

To move from the first digits to the next.

To cancel easy single digits easily.

To see the bigger picture in a matter of seconds.

How do you proceed with the Trachtenberg system?

By starting at the last significant digit and moving left.

By starting at the first significant digit and moving right.

By starting at the first significant digit and moving left.

By starting at the last significant digit and moving right.

How do you multiply by 2 with this system?

You double each digit, from right hand side.

You triple each digit, from right hand side.

You double each digit, from left hand side.

You triple each digit, from left hand side.

What's the first step when you multiply by 3?

You substract the rightmost digit from 10

You substract the rightmost digit from 5

You substract the leftmost digit from 10

You substract the rightmost digit from 3

What's the last step when you multiply by 4?

For the leading 0, you subtract 1 from half of the neighbor.

For the leading 5, you subtract 1 from half of the neighbor.

For the leading 0, you subtract 5 from half of the neighbor.

For the leading 0, you subtract 1 from the neighbor.

What's the rule for multiplying by 11?

To add the digit to its neighbor.

Quiz About The Trachtenberg System

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Quiz About The Trachtenberg System - Quiz

Have you ever wondered why some people were so good in math that they almost never needed a calculator? Well the truth is, they have a technique, and one of those techniques is called the Trachtenberg System. This system, although lengthy, consists of a number of readily memorized operations , which, in turn, allow one to perform arithmetic computations very quickly. If you're in the mood for math facts take our quiz and see how much facts you know about this technique.

Questions and Answers

1.

How is the division in the Trachtenberg system done?
- A.
  
  With multiplication
- B.
  
  With addition
- C.
  
  With subtraction
- D.
  
  With division
Correct Answer
C. With subtraction

Explanation
The division in the Trachtenberg system is done using subtraction. This method involves repeatedly subtracting the divisor from the dividend until the remainder is less than the divisor. The number of subtractions performed gives the quotient, and the final remainder is the remainder of the division. This technique is based on the principle of repeated subtraction and is an alternative approach to traditional long division.

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2.

What's the purpose of the Trachtenberg system?
- A.
  
  To find an answer in 10 seconds.
- B.
  
  To find an answer in a matter of seconds.
- C.
  
  To find an answer 1 digit at a time.
- D.
  
  To find an answer 3 digits at a time.
Correct Answer
C. To find an answer 1 digit at a time.

Explanation
The purpose of the Trachtenberg system is to find an answer 1 digit at a time. This system is a mental calculation technique that allows individuals to perform fast calculations by breaking down complex calculations into simpler ones. By solving calculations digit by digit, it becomes easier to perform calculations quickly and accurately.

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3.

What should guarantee the procedure to be effective?
- A.
  
  To keep each stage of the operation distinct.
- B.
  
  To move from the first digits to the next.
- C.
  
  To cancel easy single digits easily.
- D.
  
  To see the bigger picture in a matter of seconds.
Correct Answer
A. To keep each stage of the operation distinct.

Explanation
To ensure that the procedure is effective, it is important to keep each stage of the operation distinct. This means that each step or phase of the procedure should be clearly defined and separate from one another, allowing for a systematic and organized approach. By maintaining distinct stages, it becomes easier to track progress, identify any errors or issues, and ensure that each step is completed accurately and efficiently. This helps to avoid confusion, prevent mistakes, and ultimately increase the effectiveness of the procedure.

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4.

How do you proceed with the Trachtenberg system?
- A.
  
  By starting at the first significant digit and moving right.
- B.
  
  By starting at the first significant digit and moving left.
- C.
  
  By starting at the last significant digit and moving right.
- D.
  
  By starting at the last significant digit and moving left.
Correct Answer
D. By starting at the last significant digit and moving left.

Explanation
The Trachtenberg system is a mental calculation method that involves multiplying numbers. When using this system, you start at the last significant digit (the rightmost digit) of the number and move left, performing the necessary calculations at each digit. This method allows for quick and efficient multiplication by breaking down the process into smaller steps.

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5.

How is the digit found to the right of the digit found to the left called?
- A.
  
  Neighbor
- B.
  
  Integer
- C.
  
  The whole number
- D.
  
  A digit
Correct Answer
A. Neighbor

Explanation
The digit found to the right of the digit found to the left is called the neighbor.

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6.

How do you multiply by 2 with this system?
- A.
  
  You triple each digit, from right hand side.
- B.
  
  You double each digit, from left hand side.
- C.
  
  You double each digit, from right hand side.
- D.
  
  You triple each digit, from left hand side.
Correct Answer
C. You double each digit, from right hand side.

Explanation
In this system, to multiply by 2, you double each digit starting from the right-hand side. This means that you take each digit, multiply it by 2, and write down the result. For example, if you have the number 123, you would double the last digit (3) to get 6, then double the second digit (2) to get 4, and finally double the first digit (1) to get 2. Therefore, the result of multiplying 123 by 2 in this system would be 246.

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7.

What's the first step when you multiply by 3?
- A.
  
  You substract the rightmost digit from 5
- B.
  
  You substract the leftmost digit from 10
- C.
  
  You substract the rightmost digit from 10
- D.
  
  You substract the rightmost digit from 3
Correct Answer
C. You substract the rightmost digit from 10

Explanation
When you multiply by 3, the first step is to subtract the rightmost digit from 10. This step is necessary because when multiplying by 3, you need to carry over any excess from the previous multiplication. Subtracting the rightmost digit from 10 ensures that you are correctly accounting for any carryover.

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8.

What's the last step when you multiply by 4?
- A.
  
  For the leading 0, you subtract 1 from half of the neighbor.
- B.
  
  For the leading 5, you subtract 1 from half of the neighbor.
- C.
  
  For the leading 0, you subtract 5 from half of the neighbor.
- D.
  
  For the leading 0, you subtract 1 from the neighbor.
Correct Answer
A. For the leading 0, you subtract 1 from half of the neighbor.
9.

The first step for calculating 364*4=1384, should lead to what result?
- A.
  
  4
- B.
  
  3
- C.
  
  8
- D.
  
  12
Correct Answer
A. 4

Explanation
The first step for calculating 364*4 is to multiply the ones digit of 364 by 4, which is 16. Since 6 multiplied by 4 equals 24, we carry over the 2 and write down the 4. Therefore, the result of the first step is 4.

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10.

What's the rule for multiplying by 11?
- A.
  
  To multiply by 22
- B.
  
  To multiply by 1
- C.
  
  To add the digit to its neighbor.
- D.
  
  To multiply by 5.5
Correct Answer
C. To add the digit to its neighbor.

Explanation
To multiply by 11, the rule is to add the digit to its neighbor. This means that when multiplying a number by 11, you simply add each digit to the digit next to it. For example, if you want to multiply 25 by 11, you would add 2 and 5 together to get 7, and place it in between the original digits, resulting in 275. This rule applies to any number being multiplied by 11.

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