The tiles on the table represent the same number, no matter how they are arranged. The red rectangle represents 21 and the yellow rectangle represents 6. Together they represent 21 + 6.  

The original multiplication was  5 • 3 .  Even if we represent 5 with seven red tiles and two yellow tiles, it is still 5, and  5 • 3 = 15.  

If we add 21 + 6, the six yellow tiles cancel with six red tiles, leaving 15.   So the sub rectangles added together give the same result as the original multiplication, as it should. 

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