8. Associative property

Consider the following expressions:

 

\(P = ((-13) \times 7) \times (-4)\)

 

\(Q = (-13) \times (7 \times (-4))\)

 

\(R = ((-13) \times (-4)) \times 7\)

 

A student claims that all three expressions demonstrate the associative property of multiplication of integers.

Is the student's claim correct? Evaluate the expressions and justify your answer by identifying which expressions demonstrate the associative property.

 

Answer:

 

Student's claim : WrongCorrect

 

Value of the expressions: $P=i,Q=i,R=i$

 

The pair that demonstrates only the associative property: All threeP and QP and RR and Q

 

Reason: Both grouping and order must change to show the associative property.Any expressions having the same value show the associative property.Only the grouping of the integers changes in P and Q; their order remains unchanged.The order of the integers changes in P and Q.