How can you do e.g. 756 x 675 mentally?

  • B
  • Thread starter cyentist
  • Start date
In summary, the Trachtenberg system involves learning how to remember special numbers and then using them to solve simple math problems. It may not always work, but it can be helpful in some cases.
  • #1
cyentist
16
1
Hello!

How can you do e.g. 756 x 675 mentally?

Any good trick?
 
Mathematics news on Phys.org
  • #3
cyentist said:
Hello!

How can you do e.g. 756 x 675 mentally?

Any good trick?

To do that, you need a very good short-term memory to not lose track of what you're doing.

Something like ##999\cdot 999## is simpler because then

##(1000-1)^2 = 1000^2 + 2\cdot 1000 \cdot (-1) + (-1)^2 = 998001##

and the numbers here are "special" enough to easily keep track of.
 
  • #4
Vedic math might have some tricks to allow you to do this too but I think the Trachtenberg method is the best mentally.

https://vedicmathsindia.org/vedic-mathematics/?v=7516fd43adaa

I need to say that Vedic math is not without controversy as the name is a misnomer (ie not from the Vedic period but from a 1965 book on the subject) and its more a collection of arithmetic tricks and not math perse.

As a kid, when I was asked to do this kind of calculation by a friend, I'd ask him why he needed the answer and while he was responding, work it out mentally and then answer. It gave me a few moments but people thought my answer came out instantaneously which was okay by me.
 
  • #5
hilbert2 said:
and the numbers here are "special" enough to easily keep track of.
756*675 luckily has special enough numbers. 4*675=2700, and 756 happens to be divisible by 4. So simplifies to 189*27.
And 189 is 200-11. 11*27 is nicely 297. So 5400-297=5103. The answer is 510300.
 
  • #6
This may not always work, but does in some cases: first, use the trick for squaring : ##a^2=a^2-b^2+b^2##. Seems tautological but then factor as ##a^2=(a-b)(a+b)+b^2##. So , e.g., ##988^2=(988+12)(988-12)+12^2=(1000)(976)+144=976144##. Now, if you have either two events or two odds, e.g., if you had 756*676,you can find the average and apply the trick: 756*676= (716+40)(716-40)=##716^2-40^2##. And ##40^2=1600## and you find a convenient number to help you square 716. So this works out well with some pairs of numbers. I hope I wrote this clearly.
 
Last edited by a moderator:

1. How can you break down a large multiplication problem mentally?

One method is to break down the numbers into smaller, more manageable parts. For example, in the problem 756 x 675, you can break down 756 into 700 and 50, and 675 into 600 and 75. Then, you can multiply each part separately and then add them together to get the final answer.

2. Is there a shortcut or trick to solving large multiplication problems mentally?

Yes, there are several tricks that can help with mental multiplication. One common trick is to use the distributive property, where you break down one of the numbers into smaller parts and multiply each part by the other number. Another trick is to use rounding or estimation to get a close approximation of the answer.

3. How can you remember all the steps involved in mental multiplication?

Practice and repetition are key to remembering the steps involved in mental multiplication. It can also be helpful to write down the steps and refer to them as you practice. Over time, you will become more familiar with the process and will be able to do it without needing to write down the steps.

4. Are there any mental math techniques that can be applied to other types of math problems?

Yes, mental math techniques such as breaking down numbers, using estimation, and using the distributive property can be applied to other types of math problems, such as addition, subtraction, and division. These techniques can help make mental math easier and more efficient.

5. Can anyone learn how to do mental multiplication, or is it a skill that some people are just naturally good at?

Mental multiplication is a skill that anyone can learn with practice and dedication. While some people may have a natural aptitude for mental math, it is a skill that can be improved upon by anyone through regular practice and using different mental math strategies.

Similar threads

Replies
4
Views
544
  • General Math
Replies
2
Views
1K
Replies
10
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
946
  • Quantum Interpretations and Foundations
Replies
3
Views
1K
  • General Math
Replies
1
Views
1K
Replies
11
Views
4K
  • General Math
Replies
22
Views
1K
  • General Math
Replies
1
Views
686
Back
Top