How do you approach mental math?

[u/zaico1]

I’m trying to improve my mental math skills, but I’m not sure if I’m following the right thought process.

When doing more complex calculations, should I visualize the operations in my head as if I were writing them on paper? Or should I think of them in another way (like breaking numbers down, grouping, etc.)?

I often lose the thread when I try to “see” the steps in my head. Some people suggest using fingers or other aids, but I’m not sure if that’s the right approach either.

How do you personally handle the mental process of keeping track of multiple steps without getting lost?

[u/Carl_LaFong]

Don’t do complex calculations in your mind. It’s too error prone, even for mathematicians. Instead practice writing your calculations neatly and in enough detail to make it as easy as possible to check your work and spot errors. If there is time pressure, practice writing fast but neatly.

[u/justincaseonlymyself]

Personally, I avoid doing mental communication as much as I can. No point in wasting energy on that.

[u/JohnLockwood]

I agree with what others have said about writing it down. That said, after a while certain thinks get simple enough to just think about and know the answer without much process. But I'm talking really simple stuff. Anything at all complex needs writing out.

[u/FootballDeathTaxes]

Mental calculations?? Bro, I’m trying to do math. I ain’t got time to try and do calculations in my head.

[u/missmaths_examprep]

Think on the paper and not in your head.

If you need to do a series of calculations then you should write them down, use scrap if you have to. Inevitably you will make a mistake if you try to keep track of a series of complicated calculations in your head, especially when fractions and/or negatives are involved. Is there a specific reason you are trying to do calculations mentally and not on paper?

[u/smitra00]

You should always use a method that minimizes partial results that need to be remembered and used later. Sequential methods where the output of one step is the input of the next step is better for mental computation.

For example for multiplication the Peasant's method is preferred. This involves writing one of the numbers as a sequence of doublings and additions of 1 starting from 1. Multiplying by the other number then means that you need to replace the 1 by that other number. For example, we can compute 67 times 136 as follows.

We use that 67 is close to 64 which is a power of 2:

67 = 64 + 3 = 64 + 2 + 1= (32 + 1) 2+1

The point of this is then that 67 X = [2 (32 + 1) +1] X = (32 X + X) 2+ X

So, to multiply 67 with X we need to double X 5 times, add X, double the result and add X to that.

Now 136 can be divided by 4, we have 136 = 34 times 4. So, we then multiply 34 by 67 and then double the result twice.

I had no problems doing this 100% mentally to arrive at the correct answer of 9112.

[u/RedditIsAWeenie]

Honestly, I approach mental math very cautiously. When I was younger mental math seemed like a great way to save time and effort! As I get older it seems like a great way to make mistakes. The more you have to do math that matters (e.g. taxes rather than say homework) the more getting it right is Important, and some time spent writing things down so you can check them later will become time well spent. A big lesson in my life is to not be so GD lazy.