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Mental Subtraction

  1. Apr 4, 2010 #1
    Hello fellow maths people,

    I studied a lot of maths at uni but I'm recently into doing some mental maths. I'm wondering, does anyone have any good mental techniques for doing 3 digit subtraction? For example:


    452 - 376 =

    761 - 628 =

    432 - 259 =

    You should be able to answer each one within 4 seconds to be considered good.

    So does anyone have some good methods in their head for this? I can rarely work that fast in my head. Of course if its 430-225 its a lot easier but it's not always that simple.
  2. jcsd
  3. Apr 4, 2010 #2

    Gib Z

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    My way is kind of weird but it's what I do in my head and works well for me. The other cases reduce to very easy calculations (subtraction of 1 or 2 digit numbers) so the "harder" case is when the last two digits of A is smaller than those of B and you want A-B. When I encounter one of those, I add the right amount to both A and B to get B into a multiple of 100, then its easy.

    For your First example, id add 24 to 452, then subtract 400. If your used to it the subtracting 400 sort of happens "at the same time" as you add the 24 so it becomes quite quick.
  4. Apr 4, 2010 #3
    thanks Gib Z. That is a good idea. I guess lots of practice is also good.

    If you do 61 - 28, do you know the answer in your head immediately? Or does it take you a second or two.

    For example I may go 61 -30 + 2 so my sequence is 61..31..33

    but it takes extra time.. maybe I just need more practice so I see the numbers better.

    Tell me, how many can you answer in two minutes at the game below:?

    http://www.woodlands-junior.kent.sch.uk/maths/subhundreds120.html [Broken]
    Last edited by a moderator: May 4, 2017
  5. Apr 4, 2010 #4

    Gib Z

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    I got 22! Nothing like I was a few years ago let me tell you! I guess its all about practice and how much you encounter it in everyday life. When I was still in the lower grades of high school stuff like those came up very often, but not much anymore. I noticed though even after just 3 rounds it went up to 30. So just getting into the rhythm helps a lot.

    And yup, I do that same thing in my head for the 2 digit numbers, but the time it takes to do that is so small I can't imagine anything else being too much improvement. Just practice and you'll get better.

    Not saying practicing how to subtract quickly is the best way to spend your time all day though! lol
  6. Apr 4, 2010 #5
    Thats not bad. On the addition one I can consistently get around 30 but for subtraction I'm at around 20. All through school I relied on my calculator like nothing else so I guess I have a bit of practice to do. Its rewarding seeing improvements though. On the addition I started at around 20.
  7. Apr 4, 2010 #6

    George Jones

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    I subtract 3-digit numbers by doing addition. I look at the smaller number and "see" what I have to add to it to get the larger number. It takes me much less than four seconds.
  8. Apr 4, 2010 #7
    If you want to play mental maths look at the Trachenberg system.
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