MHB 07 division by doubling method

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The discussion focuses on using the doubling method to solve the division problem 972 divided by 69. Participants clarify the steps involved, noting that doubling 69 results in 138, and further doubling gives 276. There is confusion regarding the values of "a" and "b," particularly how "a" equals 100. The method emphasizes understanding the doubling process to simplify division. The conversation highlights the importance of clear calculations in applying the doubling method effectively.
karush
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use doubling method
$\dfrac{972}{69}$
$1 \to \boxed{69}+\boxed{a}=\boxed{?}$
$2 \to \boxed{138}+\boxed{b}=\boxed{?}$

is a 100 then what is b?
 
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Where did you get "a= 100"? The title says "doubling". I would say 69+ 69= 138, then 138+ 138= 276.
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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