Large numbers calculations

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  • #5073
    Dvora
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    Hello How can I make the calculations with large numbers such as 4-7 digits( example: 3245/6558, 2567×5869, 6422×6422) Please show the solutions and explain

    #5075
    Ofpad
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    Hi Dvora,

    The methods in the video lectures can easily be extended to 4 or 7 digit numbers.

    Bridge & Vitruvian Man Method

    You can use the bridge or the vitruvian man method for this but it is a little more complicated than 3 digit numbers. It can still be done entirely in your head if you develop a good working memory as you calculate. Only difficult part would be remembering the numbers you already calculated without writing anything down. I will show you an example.

    2567 x 5869

    Start with first set of numbers 2567 x 5869

    2 x 5 = 10

    Your answer starts with 10_ _ _ _ _ _

    Next you multiply the first set of outer pairs and add them together 2567 x 5869

    (2 x 8) + (5 x 5)  = 16 + 25 = 41

    Next digits of your answer 141_ _ _ _ _ _

    Next set of outer pairs is 2567 x 5869

    (2 x 6) + (5 x 8) + (6 x 5) = 12 + 40 + 30 = 82

    Next digits of your answer 1492 _ _ _ _ _

    Next set of outer pairs is 2567 x 5869

    (2 x 9) + (5 x 6) + (6 x 8) + (7 x 5) = 18 + 30 + 48 + 35= 131

    Next digits of your answer 15051 _ _ _ _

    Next set of outer pairs is 2567 x 5869

    (5 x 9) + (6 x 6) + (7 x 8) = 45 + 36 + 56 = 137

    Next digits of your answer 150647 _ _ _

    Next set of outer pairs is 2567 x 5869

    (6 x 9) + (7 x 6) = 54 + 42 = 96

    Next digits of your answer 1506566 _

    Last set of numbers  2567 x 5869

    7 x 9 = 63

    Next digits of your answer 15065723

    And your final answer is 15,065,723

    LR Multiplication

    You will also use the LR multiplication by rounding up the numbers. Like the following

    2567 x 5869

    5869 can be rounded up by 131 to get 6000.

    2567 x (6000 – 131) = 2567 * 6000 – 2567 * 131 = 15,402,000 – 336,277 = 15,065,723.

    Alternatively if you are comfortable doing 2 digit multiplication instead then you can round up to 5900 instead of 6000 like the following

    2567 x (5900 – 31) = 2567 * 5900 – 2567 * 31 = 15,145,300 – 79,577 = 15,065,723.

    Squaring

    You also asked for squaring 6422×6422. It can also be done for higher digits.

    Rounding down by 22

    6444 x 6400 + (22 x 22) = 6444 x 6400 + 484 = 41,242,084

    Hope this clarifies.

     

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