Math

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I need help with this problem. The question is : Find the exact value of the following expression. 6*22*5. Use any mental calculation technique you choose. Name the technique you use in each case. Here is what I have:
60*(20+2)*5 but this is where I get stumped. Can someone explain this to me. Thanks.

  • Math -

    I will show some examples and leave it to you to digest. If more explanations are needed, post again.

    Multiply without carry
    6*22*5
    =(6*5)*22
    =30*22
    =10*(3*22)
    =660

    Double and half
    6*22*5
    =6*(22*5)
    =6*(22/2)*(5*2)
    =6*11*10
    =660

    Multiply simple numbers by 11
    6*22*5
    =(6*5)*2*11
    =(30*2)*11
    =60*11
    =660

  • Math -

    mathmate you are a really smart person

  • Math -

    Isn't it amazing what brains, lots of hard work, and a good education can do for a person! :-)

  • Math -

    Thank you both for the nice comments. I love mental arithmetic, and it's one of my soft spots.

    Since it seems to arouse some interest, I will complete the explanation of the third one (multiplication by 11):

    When we multiply by 11, we only have to add adjacent digits. It's easier if there is no carry, but it can be done too. I will give an example:
    Pretend there is a imaginary zero before the first digit and after the last:
    135*11
    =(0)135(0)*11
    =(0)+1 || 1+3 || 3+5 || 5+0
    = 1 || 4 || 8 || 5
    = 1485

    With a little practice, you can do this without pen and paper.

    Try
    24513 * 11
    = 269643

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