Question

which of the following properties could be used to rewrite the expression (2/3•1/5)•5/2 as 2/3•(5/2•(5/2•1/5) sorry to ask Su many? but this test us something else

Answer 1

The original expression is given by:
 $( \frac{2}{3}*\frac{1}{5})*\frac{5}{2}$
 The correct way to rewrite the expression is given by:
 $\frac{2}{3}*(\frac{5}{2}*\frac{1}{5})$
 For this, we use two properties:

 Associative property:
 The way of grouping the factors does not change the result of the multiplication:
 $\frac{2}{3}*(\frac{1}{5}*\frac{5}{2})$

 Commutative property:
 The order of the factors does not vary the product:
 $\frac{2}{3}*(\frac{5}{2}*\frac{1}{5})$