Chapter 1.4, Problem 57STP

To determine

The property illustrated by the statement $12\cdot \left(n\cdot 5\right)=\left(12\cdot n\right)\cdot 5$ .

Answer to Problem 57STP

  $B\text{Associative Property}$

Explanation of Solution

Given information:

The properties,

  $\begin{array}{l}A\text{Commutative Property}\\ B\text{Associative Property}\\ C\text{Identity Property}\\ D\text{Zero Property}\end{array}$

Concept Used:

Commutative property:

  $a+b=b+a$

  $a\cdot b=b\cdot a$

Associative property:

  $\left(a+b\right)+c=a+\left(b+c\right)$

  $\left(a\cdot b\right)\cdot c=a\cdot \left(b\cdot c\right)$

Distributive property:

  $a\left(b+c\right)=ab+ac$

  $\left(b+c\right)a=ba+ca$

Additive identity:

  $a+0=0+a=a$

Multiplicative identity:

  $a\cdot 1=1\cdot a=a$

Zero property of Multiplication:

  $a\cdot 0=0\cdot a=0$

Calculation:

Here in the given statement, observe that sequence of the multiplication of first two numbers is change in the right side. It is of the form $a\cdot \left(b\cdot c\right)=\left(a\cdot b\right)\cdot c$ . So, the property shown by the given statement is associative property of multiplication.

Thus, the given statement shows the associative property.