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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
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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