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Properties
Why is a X b always equal to b X a ?
Visualization: Draw a grid with a rows and b columns and rotate the page 90 degress so that the rows appear as columns and columns appear as rows. Now we have b rows and a columns.
a X b = a times b 's = b times a 's = b X a .
If a X b = c then why is c ÷ a = b and c ÷ b = a ?
Note: a times b 's = b times a 's = c .
Visualization: Draw a grid with a rows and b columns, or; b rows and a columns.
If we repeatedly take away b 's then that can be done a times. Therefore c ÷ b = a .
If we repeatedly take away a 's then that can be done b times. Therefore c ÷ a = b .
Properties
If t chocolates are distributed among n students, how many choclates each student will get?
Visualization: Distributing equally.
Visualization: Repeatedly subtracting n chocolates from t chocolates so that each student gets one.
t ÷ n .
If each student should get n chocolates. How many students will get chocolates if there are t chocolates?
Visualization: Repeatedly subtracting n chocolates from t chocolates because each student should get n chocolates.
t ÷ n .
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