Is A Always Equal to B? Understanding Equality in Math

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In mathematics, the equation (1 / 1) = (B / A) = (A = B) holds true provided that A is not equal to zero. This can be simplified to the expression B/A = 1, which leads to the conclusion that B equals A. The discussion emphasizes the importance of A being non-zero for the equality to be valid. Understanding this relationship is crucial for grasping fundamental concepts of equality in math. Therefore, A always equals B when A is not zero.
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( 1 / 1 ) = ( B / A ) = ( A = B )
 
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That's is in fact true as long as A does not equal 0. It can be simplified to:

\frac{B}{A} = 1 \; \text{for $ A \neq 0$} \quad \text{hence} \quad B = A
 

Thread 'Area of Overlapping Squares'

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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