We are given the following expression
[tex]-\frac{1}{3}-10+7+\frac{2}{3}+5[/tex]We are asked which of the given option shows the best use of associative and commutative properties to simplify the above expression?
Let us first have a look at associative and commutative properties of addition.
Associative property of addition:
[tex]a+(b+c)=(a+b)+c[/tex]Which states that when you add you can group numbers in any order.
Commutative property of addition:
[tex]a+b=b+a[/tex]Which states that you can add in any order, the result would always be the same.
Option A is given by
[tex](-\frac{1}{3}+\frac{2}{3})+\lbrack5+7+(-10)\rbrack[/tex]As you can see, the first part covers the commutative property and the second part covers the associative property.
We simply grouped the fractional parts together and also grouped the integers together.
Remember that you can group numbers in any order, the result would always be the same.
Therefore, option A seems to be the best use of associative and commutative properties to simplify the given expression.