Chapter 1.4, Problem 55STP

To determine

Out of the given statements, which statement is an example of identity property.

Answer to Problem 55STP

  $D4x+0=4x$

Explanation of Solution

Given information:

The statements,

  $\begin{array}{l}A3\cdot x\cdot 0=0\\ B7\left(4x\right)=\left(4\cdot 7\right)x\\ C5+\left(4+x\right)=\left(5+4\right)+x\\ D4x+0=4x\end{array}$

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:

Observe that the identity properties are of two types, one is the multiplicative identity which is when any number or expression multiplied to 1 gives the result itself.

And the other is additive identity which is when any number or expression get added with 0 will result in itself again.

From the given statements only the last statement is an example of identity property because 0 is added with 4x is qual to 4x. So, it is an example of additive identity.

Thus, the statement $D4x+0=4x$ is an example of the identity property.